Question: What shows the graph of a function with all it's salient parts?

Answer: sketch

The graph of a function or relation is the set of all points satisfying that function or relation. For a function of one variable, f, the set of all points (x, y), where y = f(x) is the graph of the function f. For a function g of two variables, the set of all points (x, y, z), where z = g(x, y) is the graph of the function g. <hl> A sketch of the graph of such a function or relation would consist of all the salient parts of the function or relation which would include its relative extrema, its concavity and points of inflection, any points of discontinuity and its end behavior. <hl> All of these terms are more fully defined in calculus. Such graphs are useful in calculus to understand the nature and behavior of a function or relation.

The graph of a function or relation is the set of all points satisfying that function or relation. For a function of one variable, f, the set of all points (x, y), where y = f(x) is the graph of the function f. For a function g of two variables, the set of all points (x, y, z), where z = g(x, y) is the graph of the function g. A <hl> sketch <hl> of the graph of such a function or relation would consist of all the salient parts of the function or relation which would include its relative extrema, its concavity and points of inflection, any points of discontinuity and its end behavior. All of these terms are more fully defined in calculus. Such graphs are useful in calculus to understand the nature and behavior of a function or relation.


Question: Relative extrema, concavity, points of inflection, and points of discontibuity are fully defined in what?

The graph of a function or relation is the set of all points satisfying that function or relation. For a function of one variable, f, the set of all points (x, y), where y = f(x) is the graph of the function f. For a function g of two variables, the set of all points (x, y, z), where z = g(x, y) is the graph of the function g. A sketch of the graph of such a function or relation would consist of all the salient parts of the function or relation which would include its relative extrema, its concavity and points of inflection, any points of discontinuity and its end behavior. All of these terms are more fully defined in calculus. Such graphs are useful in calculus to understand the nature and behavior of a function or relation.

Answer: calculus

The graph of a function or relation is the set of all points satisfying that function or relation. For a function of one variable, f, the set of all points (x, y), where y = f(x) is the graph of the function f. For a function g of two variables, the set of all points (x, y, z), where z = g(x, y) is the graph of the function g. A sketch of the graph of such a function or relation would consist of all the salient parts of the function or relation which would include its relative extrema, its concavity and points of inflection, any points of discontinuity and its end behavior. <hl> All of these terms are more fully defined in calculus . <hl> Such graphs are useful in calculus to understand the nature and behavior of a function or relation.

The graph of a function or relation is the set of all points satisfying that function or relation. For a function of one variable, f, the set of all points (x, y), where y = f(x) is the graph of the function f. For a function g of two variables, the set of all points (x, y, z), where z = g(x, y) is the graph of the function g. A sketch of the graph of such a function or relation would consist of all the salient parts of the function or relation which would include its relative extrema, its concavity and points of inflection, any points of discontinuity and its end behavior. All of these terms are more fully defined in <hl> calculus <hl>. Such graphs are useful in calculus to understand the nature and behavior of a function or relation.

All of these terms are more fully defined in <hl> calculus <hl> .


Question: Graphs are useful in calculus to understand the nature and behavior of what?

Answer: a function or relation

<hl> The graph of a function or relation is the set of all points satisfying that function or relation. <hl> For a function of one variable, f, the set of all points (x, y), where y = f(x) is the graph of the function f. For a function g of two variables, the set of all points (x, y, z), where z = g(x, y) is the graph of the function g. A sketch of the graph of such a function or relation would consist of all the salient parts of the function or relation which would include its relative extrema, its concavity and points of inflection, any points of discontinuity and its end behavior. All of these terms are more fully defined in calculus. Such graphs are useful in calculus to understand the nature and behavior of a function or relation.

The graph of <hl> a function or relation <hl> is the set of all points satisfying that function or relation. For a function of one variable, f, the set of all points (x, y), where y = f(x) is the graph of the function f. For a function g of two variables, the set of all points (x, y, z), where z = g(x, y) is the graph of the function g. A sketch of the graph of such a function or relation would consist of all the salient parts of the function or relation which would include its relative extrema, its concavity and points of inflection, any points of discontinuity and its end behavior. All of these terms are more fully defined in calculus. Such graphs are useful in calculus to understand the nature and behavior of a function or relation.


Question: Point O refers to what on the line?

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Answer: origin

<hl> Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin ), a unit of length, and an orientation for the line. <hl> An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the <hl> origin <hl>), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the <hl> origin <hl> ), a unit of length, and an orientation for the line.


Question: An orientation involves one positive and one what?

Answer: negative

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. <hl> An orientation chooses which of the two half-lines determined by O is the positive, and which is negative ; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. <hl> Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is <hl> negative <hl>; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

An orientation chooses which of the two half-lines determined by O is the positive, and which is <hl> negative <hl> ; we then say that the line "is oriented" (or "points") from the negative half towards the positive half.


Question: How many dimensions does a single straight line exist in?

Answer: one

<hl> Choosing a Cartesian coordinate system for a one -dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. <hl> An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a <hl> one <hl>-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a <hl> one <hl> -dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line.


Question: The distance of P can be specified from what point?

Answer: its distance from O,

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. <hl> Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P. <hl>

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by <hl> its distance from O, <hl> taken with a + or − sign depending on which half-line contains P.


Question: What is a one-dimensional space called?

Answer: a straight line

<hl> Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line —involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. <hl> An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for <hl> a straight line <hl>—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for <hl> a straight line <hl> —involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line.


Question: The origin of the line is a unit of what?

Answer: length

<hl> Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length , and an orientation for the line. <hl> An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of <hl> length <hl>, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of <hl> length <hl> , and an orientation for the line.


Question: What determines which half-line is positive and which is negative?

Answer: An orientation

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. <hl> An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. <hl> Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. <hl> An orientation <hl> chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.


Question: What is point O?

Answer: the origin

<hl> Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line ( the origin ), a unit of length, and an orientation for the line. <hl> An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (<hl> the origin <hl>), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line ( <hl> the origin <hl> ), a unit of length, and an orientation for the line.


Question: What is another term for "is oriented"?

Answer: points

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. <hl> An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or " points ") from the negative half towards the positive half. <hl> Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "<hl> points <hl>") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P.

An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or " <hl> points <hl> ") from the negative half towards the positive half.


Question: The Cartesian coordinate system in two dimensions can also be referred to as what?

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

Answer: rectangular coordinate system

<hl> The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system ) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. <hl> (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The Cartesian coordinate system in two dimensions (also called a <hl> rectangular coordinate system <hl>) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The Cartesian coordinate system in two dimensions (also called a <hl> rectangular coordinate system <hl> ) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.


Question: What kind of axes do not meet at right angles?

Answer: oblique

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. <hl> (Early systems allowed " oblique " axes, that is, axes that did not meet at right angles.) <hl> The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "<hl> oblique <hl>" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

(Early systems allowed " <hl> oblique <hl> " axes, that is, axes that did not meet at right angles.)


Question: A pair of x and y refer to what variable?

Answer: the x-axis is taken to be horizontal and the y-axis is taken to be vertical.

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) <hl> The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. <hl> For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where <hl> the x-axis is taken to be horizontal and the y-axis is taken to be vertical. <hl> The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).


Question: X-axis refers to what direction?

Answer: horizontal

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) <hl> The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. <hl> The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be <hl> horizontal <hl> and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).


Question: What direction does y-axis refer to?

Answer: vertical

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) <hl> The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical . <hl> The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be <hl> vertical <hl>. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be <hl> vertical <hl> .


Question: What is a two-dimensional space called?

Answer: rectangular coordinate system

<hl> The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system ) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. <hl> (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The Cartesian coordinate system in two dimensions (also called a <hl> rectangular coordinate system <hl>) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The Cartesian coordinate system in two dimensions (also called a <hl> rectangular coordinate system <hl> ) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.


Question: What is the point where the axes meet?

Answer: the origin for both

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. <hl> The point where the axes meet is taken as the origin for both , thus turning each axis into a number line. <hl> For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as <hl> the origin for both <hl>, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The point where the axes meet is taken as <hl> the origin for both <hl> , thus turning each axis into a number line.


Question: How is a rectangular coordinate system defined?

Answer: is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.

<hl> The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) <hl> The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) <hl> is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. <hl> (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).


Question: What did early systems allow?

Answer: oblique" axes, that is, axes that did not meet at right angles

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. <hl> (Early systems allowed " oblique" axes, that is, axes that did not meet at right angles .) <hl> The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

The Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. (Early systems allowed "<hl> oblique" axes, that is, axes that did not meet at right angles <hl>.) The lines are commonly referred to as the x- and y-axes where the x-axis is taken to be horizontal and the y-axis is taken to be vertical. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For a given point P, a line is drawn through P perpendicular to the x-axis to meet it at X and second line is drawn through P perpendicular to the y-axis to meet it at Y. The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines. The coordinates are written as an ordered pair (x, y).

(Early systems allowed " <hl> oblique" axes, that is, axes that did not meet at right angles <hl> .)


Question: What do you choose for a three-dimensional space?

Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes) that are pair-wise perpendicular, have a single unit of length for all three axes and have an orientation for each axis.  As in the two-dimensional case, each axis becomes a number line.  The coordinates of a point P are obtained by drawing a line through P perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.

Answer: an ordered triplet of lines (axes) that are pair-wise perpendicular, have a single unit of length for all three axes and have an orientation for each axis.

<hl> Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes) that are pair-wise perpendicular, have a single unit of length for all three axes and have an orientation for each axis. As in the two-dimensional case, each axis becomes a number line. <hl> The coordinates of a point P are obtained by drawing a line through P perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.

Choosing a Cartesian coordinate system for a three-dimensional space means choosing <hl> an ordered triplet of lines (axes) that are pair-wise perpendicular, have a single unit of length for all three axes and have an orientation for each axis. <hl> As in the two-dimensional case, each axis becomes a number line. The coordinates of a point P are obtained by drawing a line through P perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.


Question: How many units of length are there for all three axes?

Answer: a single unit of length

<hl> Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes) that are pair-wise perpendicular, have a single unit of length for all three axes and have an orientation for each axis. <hl> As in the two-dimensional case, each axis becomes a number line. The coordinates of a point P are obtained by drawing a line through P perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.

Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes) that are pair-wise perpendicular, have <hl> a single unit of length <hl> for all three axes and have an orientation for each axis. As in the two-dimensional case, each axis becomes a number line. The coordinates of a point P are obtained by drawing a line through P perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.


Question: Do you find the the coordinates of a point P by drawing a line parallel or perpendicular?

Answer: perpendicular

<hl> Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes) that are pair-wise perpendicular , have a single unit of length for all three axes and have an orientation for each axis. <hl> As in the two-dimensional case, each axis becomes a number line. The coordinates of a point P are obtained by drawing a line through P perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.

Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes) that are pair-wise <hl> perpendicular <hl>, have a single unit of length for all three axes and have an orientation for each axis. As in the two-dimensional case, each axis becomes a number line. The coordinates of a point P are obtained by drawing a line through P perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.

Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes) that are pair-wise <hl> perpendicular <hl> , have a single unit of length for all three axes and have an orientation for each axis.


Question: What does each axis become?

Answer: a number line

Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes) that are pair-wise perpendicular, have a single unit of length for all three axes and have an orientation for each axis. <hl> As in the two-dimensional case, each axis becomes a number line . <hl> The coordinates of a point P are obtained by drawing a line through P perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.

Choosing a Cartesian coordinate system for a three-dimensional space means choosing an ordered triplet of lines (axes) that are pair-wise perpendicular, have a single unit of length for all three axes and have an orientation for each axis. As in the two-dimensional case, each axis becomes <hl> a number line <hl>. The coordinates of a point P are obtained by drawing a line through P perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.

As in the two-dimensional case, each axis becomes <hl> a number line <hl> .


Question: What is a Euclidean plane with a Cartesian system called?

A Euclidean plane with a chosen Cartesian system is called a Cartesian plane.  Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product

R

2

=

R

×

R

{\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} }

, where

R

{\displaystyle \mathbb {R} }

 is the set of all reals.  In the same way, the points any Euclidean space of dimension n  be identified with the tuples (lists) of n real numbers, that is, with the Cartesian product

R

n

{\displaystyle \mathbb {R} ^{n}}

.

Answer: a Cartesian plane.

<hl> A Euclidean plane with a chosen Cartesian system is called a Cartesian plane. Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} } is the set of all reals. <hl> In the same way, the points any Euclidean space of dimension n be identified with the tuples (lists) of n real numbers, that is, with the Cartesian product R n {\displaystyle \mathbb {R} ^{n}} .

A Euclidean plane with a chosen Cartesian system is called <hl> a Cartesian plane. <hl> Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} } is the set of all reals. In the same way, the points any Euclidean space of dimension n be identified with the tuples (lists) of n real numbers, that is, with the Cartesian product R n {\displaystyle \mathbb {R} ^{n}} .


Question: The points of a Cartesian plan can be identified with what?

Answer: pairs of real numbers

A Euclidean plane with a chosen Cartesian system is called a Cartesian plane. <hl> Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers ; that is with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} } is the set of all reals. <hl> In the same way, the points any Euclidean space of dimension n be identified with the tuples (lists) of n real numbers, that is, with the Cartesian product R n {\displaystyle \mathbb {R} ^{n}} .

A Euclidean plane with a chosen Cartesian system is called a Cartesian plane. Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with <hl> pairs of real numbers <hl>; that is with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} } is the set of all reals. In the same way, the points any Euclidean space of dimension n be identified with the tuples (lists) of n real numbers, that is, with the Cartesian product R n {\displaystyle \mathbb {R} ^{n}} .

Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with <hl> pairs of real numbers <hl> ; that is with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} } is the set of all reals.


Question: What is another name for tuples?

Answer: lists

A Euclidean plane with a chosen Cartesian system is called a Cartesian plane. Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} } is the set of all reals. <hl> In the same way, the points any Euclidean space of dimension n be identified with the tuples ( lists ) of n real numbers, <hl> that is, with the Cartesian product R n {\displaystyle \mathbb {R} ^{n}} .

A Euclidean plane with a chosen Cartesian system is called a Cartesian plane. Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} } is the set of all reals. In the same way, the points any Euclidean space of dimension n be identified with the tuples (<hl> lists <hl>) of n real numbers, that is, with the Cartesian product R n {\displaystyle \mathbb {R} ^{n}} .

In the same way, the points any Euclidean space of dimension n be identified with the tuples ( <hl> lists <hl> ) of n real numbers,


Question: Are Cartesian coordinates similar?

Answer: Cartesian coordinates are unique and non-ambiguous

A Euclidean plane with a chosen Cartesian system is called a Cartesian plane. <hl> Since Cartesian coordinates are unique and non-ambiguous , the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} } is the set of all reals. <hl> In the same way, the points any Euclidean space of dimension n be identified with the tuples (lists) of n real numbers, that is, with the Cartesian product R n {\displaystyle \mathbb {R} ^{n}} .

A Euclidean plane with a chosen Cartesian system is called a Cartesian plane. Since <hl> Cartesian coordinates are unique and non-ambiguous <hl>, the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} } is the set of all reals. In the same way, the points any Euclidean space of dimension n be identified with the tuples (lists) of n real numbers, that is, with the Cartesian product R n {\displaystyle \mathbb {R} ^{n}} .

Since <hl> Cartesian coordinates are unique and non-ambiguous <hl> , the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} } is the set of all reals.


Question: What does a Cartesian coordinate allow?

The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis.  In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see Affine plane).

Answer: allow axes that are not perpendicular to each other, and/or different units along each axis

<hl> The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis . <hl> In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see Affine plane).

The concept of Cartesian coordinates generalizes to <hl> allow axes that are not perpendicular to each other, and/or different units along each axis <hl>. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see Affine plane).

The concept of Cartesian coordinates generalizes to <hl> allow axes that are not perpendicular to each other, and/or different units along each axis <hl> .


Question: How is each coordinate obtained?

Answer: by projecting the point onto one axis along a direction that is parallel to the other axis

The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis. <hl> In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). <hl> In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see Affine plane).

The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained <hl> by projecting the point onto one axis along a direction that is parallel to the other axis <hl> (or, in general, to the hyperplane defined by all the other axes). In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see Affine plane).


Question: What must be modified in an oblique coordinate system?

Answer: the computations of distances and angles

The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). <hl> In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see Affine plane). <hl>

The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In such an oblique coordinate system <hl> the computations of distances and angles <hl> must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see Affine plane).


Question: The formula for distance is called what?

Answer: the Pythagorean formula

The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). <hl> In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see Affine plane). <hl>

The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as <hl> the Pythagorean formula <hl> for the distance) do not hold (see Affine plane).


Question: What's the symbol for Tin?

Tin is a chemical element with the symbol Sn (for Latin: stannum) and atomic number 50. It is a main group metal in group 14 of the periodic table. Tin shows a chemical similarity to both neighboring group-14 elements, germanium and lead, and has two possible oxidation states, +2 and the slightly more stable +4. Tin is the 49th most abundant element and has, with 10 stable isotopes, the largest number of stable isotopes in the periodic table. It is a silvery, malleable other metal that is not easily oxidized in air, obtained chiefly from the mineral cassiterite where it occurs as tin dioxide, SnO2.

Answer: symbol Sn

<hl> Tin is a chemical element with the symbol Sn (for Latin: stannum) and atomic number 50. <hl> It is a main group metal in group 14 of the periodic table. Tin shows a chemical similarity to both neighboring group-14 elements, germanium and lead, and has two possible oxidation states, +2 and the slightly more stable +4. Tin is the 49th most abundant element and has, with 10 stable isotopes, the largest number of stable isotopes in the periodic table. It is a silvery, malleable other metal that is not easily oxidized in air, obtained chiefly from the mineral cassiterite where it occurs as tin dioxide, SnO2.

Tin is a chemical element with the <hl> symbol Sn <hl> (for Latin: stannum) and atomic number 50. It is a main group metal in group 14 of the periodic table. Tin shows a chemical similarity to both neighboring group-14 elements, germanium and lead, and has two possible oxidation states, +2 and the slightly more stable +4. Tin is the 49th most abundant element and has, with 10 stable isotopes, the largest number of stable isotopes in the periodic table. It is a silvery, malleable other metal that is not easily oxidized in air, obtained chiefly from the mineral cassiterite where it occurs as tin dioxide, SnO2.


Question: How many isotopes does Tin have?

Answer: 10 stable isotopes

Tin is a chemical element with the symbol Sn (for Latin: stannum) and atomic number 50. It is a main group metal in group 14 of the periodic table. Tin shows a chemical similarity to both neighboring group-14 elements, germanium and lead, and has two possible oxidation states, +2 and the slightly more stable +4. <hl> Tin is the 49th most abundant element and has, with 10 stable isotopes , the largest number of stable isotopes in the periodic table. <hl> It is a silvery, malleable other metal that is not easily oxidized in air, obtained chiefly from the mineral cassiterite where it occurs as tin dioxide, SnO2.

Tin is a chemical element with the symbol Sn (for Latin: stannum) and atomic number 50. It is a main group metal in group 14 of the periodic table. Tin shows a chemical similarity to both neighboring group-14 elements, germanium and lead, and has two possible oxidation states, +2 and the slightly more stable +4. Tin is the 49th most abundant element and has, with <hl> 10 stable isotopes <hl>, the largest number of stable isotopes in the periodic table. It is a silvery, malleable other metal that is not easily oxidized in air, obtained chiefly from the mineral cassiterite where it occurs as tin dioxide, SnO2.

Tin is the 49th most abundant element and has, with <hl> 10 stable isotopes <hl> , the largest number of stable isotopes in the periodic table.


Question: What is Tin similar to?

Answer: germanium and lead

Tin is a chemical element with the symbol Sn (for Latin: stannum) and atomic number 50. It is a main group metal in group 14 of the periodic table. <hl> Tin shows a chemical similarity to both neighboring group-14 elements, germanium and lead , and has two possible oxidation states, +2 and the slightly more stable +4. <hl> Tin is the 49th most abundant element and has, with 10 stable isotopes, the largest number of stable isotopes in the periodic table. It is a silvery, malleable other metal that is not easily oxidized in air, obtained chiefly from the mineral cassiterite where it occurs as tin dioxide, SnO2.

Tin is a chemical element with the symbol Sn (for Latin: stannum) and atomic number 50. It is a main group metal in group 14 of the periodic table. Tin shows a chemical similarity to both neighboring group-14 elements, <hl> germanium and lead <hl>, and has two possible oxidation states, +2 and the slightly more stable +4. Tin is the 49th most abundant element and has, with 10 stable isotopes, the largest number of stable isotopes in the periodic table. It is a silvery, malleable other metal that is not easily oxidized in air, obtained chiefly from the mineral cassiterite where it occurs as tin dioxide, SnO2.

Tin shows a chemical similarity to both neighboring group-14 elements, <hl> germanium and lead <hl> , and has two possible oxidation states, +2 and the slightly more stable +4.


Question: How do you obtain Tin?

Answer: obtained chiefly from the mineral cassiterite

Tin is a chemical element with the symbol Sn (for Latin: stannum) and atomic number 50. It is a main group metal in group 14 of the periodic table. Tin shows a chemical similarity to both neighboring group-14 elements, germanium and lead, and has two possible oxidation states, +2 and the slightly more stable +4. Tin is the 49th most abundant element and has, with 10 stable isotopes, the largest number of stable isotopes in the periodic table. <hl> It is a silvery, malleable other metal that is not easily oxidized in air, obtained chiefly from the mineral cassiterite where it occurs as tin dioxide, SnO2. <hl>

Tin is a chemical element with the symbol Sn (for Latin: stannum) and atomic number 50. It is a main group metal in group 14 of the periodic table. Tin shows a chemical similarity to both neighboring group-14 elements, germanium and lead, and has two possible oxidation states, +2 and the slightly more stable +4. Tin is the 49th most abundant element and has, with 10 stable isotopes, the largest number of stable isotopes in the periodic table. It is a silvery, malleable other metal that is not easily oxidized in air, <hl> obtained chiefly from the mineral cassiterite <hl> where it occurs as tin dioxide, SnO2.


Question: Does Tin have oxidation states?

Answer: has two possible oxidation states, +2 and the slightly more stable +4

Tin is a chemical element with the symbol Sn (for Latin: stannum) and atomic number 50. It is a main group metal in group 14 of the periodic table. <hl> Tin shows a chemical similarity to both neighboring group-14 elements, germanium and lead, and has two possible oxidation states, +2 and the slightly more stable +4 . <hl> Tin is the 49th most abundant element and has, with 10 stable isotopes, the largest number of stable isotopes in the periodic table. It is a silvery, malleable other metal that is not easily oxidized in air, obtained chiefly from the mineral cassiterite where it occurs as tin dioxide, SnO2.

Tin is a chemical element with the symbol Sn (for Latin: stannum) and atomic number 50. It is a main group metal in group 14 of the periodic table. Tin shows a chemical similarity to both neighboring group-14 elements, germanium and lead, and <hl> has two possible oxidation states, +2 and the slightly more stable +4 <hl>. Tin is the 49th most abundant element and has, with 10 stable isotopes, the largest number of stable isotopes in the periodic table. It is a silvery, malleable other metal that is not easily oxidized in air, obtained chiefly from the mineral cassiterite where it occurs as tin dioxide, SnO2.

Tin shows a chemical similarity to both neighboring group-14 elements, germanium and lead, and <hl> has two possible oxidation states, +2 and the slightly more stable +4 <hl> .


Question: What was the first alloy used on a large scale?

The first alloy used on a large scale since 3000 BC was bronze, an alloy of tin and copper. After 600 BC, pure metallic tin was produced. Pewter, which is an alloy of 85–90% tin with the remainder commonly consisting of copper, antimony and lead, was used for flatware from the Bronze Age until the 20th century. In modern times, tin is used in many alloys, most notably tin/lead soft solders, which are typically 60% or more tin. Another large application for tin is corrosion-resistant tin plating of steel. Because of its low toxicity, tin-plated metal was used for food packaging as tin cans, which are now made mostly of steel,[citation needed] even though the name is kept in English.

Answer: The first alloy used on a large scale since 3000 BC was bronze

<hl> The first alloy used on a large scale since 3000 BC was bronze , an alloy of tin and copper. <hl> After 600 BC, pure metallic tin was produced. Pewter, which is an alloy of 85–90% tin with the remainder commonly consisting of copper, antimony and lead, was used for flatware from the Bronze Age until the 20th century. In modern times, tin is used in many alloys, most notably tin/lead soft solders, which are typically 60% or more tin. Another large application for tin is corrosion-resistant tin plating of steel. Because of its low toxicity, tin-plated metal was used for food packaging as tin cans, which are now made mostly of steel,[citation needed] even though the name is kept in English.

<hl> The first alloy used on a large scale since 3000 BC was bronze <hl>, an alloy of tin and copper. After 600 BC, pure metallic tin was produced. Pewter, which is an alloy of 85–90% tin with the remainder commonly consisting of copper, antimony and lead, was used for flatware from the Bronze Age until the 20th century. In modern times, tin is used in many alloys, most notably tin/lead soft solders, which are typically 60% or more tin. Another large application for tin is corrosion-resistant tin plating of steel. Because of its low toxicity, tin-plated metal was used for food packaging as tin cans, which are now made mostly of steel,[citation needed] even though the name is kept in English.

<hl> The first alloy used on a large scale since 3000 BC was bronze <hl> , an alloy of tin and copper.


Question: What is a big application for tin?

Answer: corrosion-resistant tin plating of steel

The first alloy used on a large scale since 3000 BC was bronze, an alloy of tin and copper. After 600 BC, pure metallic tin was produced. Pewter, which is an alloy of 85–90% tin with the remainder commonly consisting of copper, antimony and lead, was used for flatware from the Bronze Age until the 20th century. In modern times, tin is used in many alloys, most notably tin/lead soft solders, which are typically 60% or more tin. <hl> Another large application for tin is corrosion-resistant tin plating of steel . <hl> Because of its low toxicity, tin-plated metal was used for food packaging as tin cans, which are now made mostly of steel,[citation needed] even though the name is kept in English.

The first alloy used on a large scale since 3000 BC was bronze, an alloy of tin and copper. After 600 BC, pure metallic tin was produced. Pewter, which is an alloy of 85–90% tin with the remainder commonly consisting of copper, antimony and lead, was used for flatware from the Bronze Age until the 20th century. In modern times, tin is used in many alloys, most notably tin/lead soft solders, which are typically 60% or more tin. Another large application for tin is <hl> corrosion-resistant tin plating of steel <hl>. Because of its low toxicity, tin-plated metal was used for food packaging as tin cans, which are now made mostly of steel,[citation needed] even though the name is kept in English.

Another large application for tin is <hl> corrosion-resistant tin plating of steel <hl> .


Question: What was Pewter used for?

Answer: was used for flatware from the Bronze Age until the 20th century

The first alloy used on a large scale since 3000 BC was bronze, an alloy of tin and copper. After 600 BC, pure metallic tin was produced. <hl> Pewter, which is an alloy of 85–90% tin with the remainder commonly consisting of copper, antimony and lead, was used for flatware from the Bronze Age until the 20th century . <hl> In modern times, tin is used in many alloys, most notably tin/lead soft solders, which are typically 60% or more tin. Another large application for tin is corrosion-resistant tin plating of steel. Because of its low toxicity, tin-plated metal was used for food packaging as tin cans, which are now made mostly of steel,[citation needed] even though the name is kept in English.

The first alloy used on a large scale since 3000 BC was bronze, an alloy of tin and copper. After 600 BC, pure metallic tin was produced. Pewter, which is an alloy of 85–90% tin with the remainder commonly consisting of copper, antimony and lead, <hl> was used for flatware from the Bronze Age until the 20th century <hl>. In modern times, tin is used in many alloys, most notably tin/lead soft solders, which are typically 60% or more tin. Another large application for tin is corrosion-resistant tin plating of steel. Because of its low toxicity, tin-plated metal was used for food packaging as tin cans, which are now made mostly of steel,[citation needed] even though the name is kept in English.

Pewter, which is an alloy of 85–90% tin with the remainder commonly consisting of copper, antimony and lead, <hl> was used for flatware from the Bronze Age until the 20th century <hl> .


Question: What was tin used for?

Answer: tin-plated metal was used for food packaging as tin cans

The first alloy used on a large scale since 3000 BC was bronze, an alloy of tin and copper. After 600 BC, pure metallic tin was produced. Pewter, which is an alloy of 85–90% tin with the remainder commonly consisting of copper, antimony and lead, was used for flatware from the Bronze Age until the 20th century. In modern times, tin is used in many alloys, most notably tin/lead soft solders, which are typically 60% or more tin. Another large application for tin is corrosion-resistant tin plating of steel. <hl> Because of its low toxicity, tin-plated metal was used for food packaging as tin cans , which are now made mostly of steel,[citation needed] even though the name is kept in English. <hl>

The first alloy used on a large scale since 3000 BC was bronze, an alloy of tin and copper. After 600 BC, pure metallic tin was produced. Pewter, which is an alloy of 85–90% tin with the remainder commonly consisting of copper, antimony and lead, was used for flatware from the Bronze Age until the 20th century. In modern times, tin is used in many alloys, most notably tin/lead soft solders, which are typically 60% or more tin. Another large application for tin is corrosion-resistant tin plating of steel. Because of its low toxicity, <hl> tin-plated metal was used for food packaging as tin cans <hl>, which are now made mostly of steel,[citation needed] even though the name is kept in English.

Because of its low toxicity, <hl> tin-plated metal was used for food packaging as tin cans <hl> , which are now made mostly of steel,[citation needed] even though the name is kept in English.


Question: What is tin?

Tin is a malleable, ductile and highly crystalline silvery-white metal. When a bar of tin is bent, a crackling sound known as the tin cry can be heard due to the twinning of the crystals. Tin melts at a low temperature of about 232 °C (450 °F), which is further reduced to 177.3 °C (351.1 °F) for 11 nm particles.

Answer: Tin is a malleable, ductile and highly crystalline silvery-white metal.

<hl> Tin is a malleable, ductile and highly crystalline silvery-white metal. When a bar of tin is bent, a crackling sound known as the tin cry can be heard due to the twinning of the crystals. <hl> Tin melts at a low temperature of about 232 °C (450 °F), which is further reduced to 177.3 °C (351.1 °F) for 11 nm particles.

<hl> Tin is a malleable, ductile and highly crystalline silvery-white metal. <hl> When a bar of tin is bent, a crackling sound known as the tin cry can be heard due to the twinning of the crystals. Tin melts at a low temperature of about 232 °C (450 °F), which is further reduced to 177.3 °C (351.1 °F) for 11 nm particles.


Question: At what temperature does tin melt?

Answer: Tin melts at a low temperature of about 232 °C (450 °F)

Tin is a malleable, ductile and highly crystalline silvery-white metal. When a bar of tin is bent, a crackling sound known as the tin cry can be heard due to the twinning of the crystals. <hl> Tin melts at a low temperature of about 232 °C (450 °F) , which is further reduced to 177.3 °C (351.1 °F) for 11 nm particles. <hl>

Tin is a malleable, ductile and highly crystalline silvery-white metal. When a bar of tin is bent, a crackling sound known as the tin cry can be heard due to the twinning of the crystals. <hl> Tin melts at a low temperature of about 232 °C (450 °F) <hl>, which is further reduced to 177.3 °C (351.1 °F) for 11 nm particles.

<hl> Tin melts at a low temperature of about 232 °C (450 °F) <hl> , which is further reduced to 177.3 °C (351.1 °F) for 11 nm particles.


Question: Why does bending tin make noise?

Answer: a crackling sound known as the tin cry can be heard due to the twinning of the crystals

Tin is a malleable, ductile and highly crystalline silvery-white metal. <hl> When a bar of tin is bent, a crackling sound known as the tin cry can be heard due to the twinning of the crystals . <hl> Tin melts at a low temperature of about 232 °C (450 °F), which is further reduced to 177.3 °C (351.1 °F) for 11 nm particles.

Tin is a malleable, ductile and highly crystalline silvery-white metal. When a bar of tin is bent, <hl> a crackling sound known as the tin cry can be heard due to the twinning of the crystals <hl>. Tin melts at a low temperature of about 232 °C (450 °F), which is further reduced to 177.3 °C (351.1 °F) for 11 nm particles.

When a bar of tin is bent, <hl> a crackling sound known as the tin cry can be heard due to the twinning of the crystals <hl> .


Question: What's the lowest temperature tin reaches?

Answer: 177.3 °C (351.1 °F) for 11 nm particles

Tin is a malleable, ductile and highly crystalline silvery-white metal. When a bar of tin is bent, a crackling sound known as the tin cry can be heard due to the twinning of the crystals. <hl> Tin melts at a low temperature of about 232 °C (450 °F), which is further reduced to 177.3 °C (351.1 °F) for 11 nm particles . <hl>

Tin is a malleable, ductile and highly crystalline silvery-white metal. When a bar of tin is bent, a crackling sound known as the tin cry can be heard due to the twinning of the crystals. Tin melts at a low temperature of about 232 °C (450 °F), which is further reduced to <hl> 177.3 °C (351.1 °F) for 11 nm particles <hl>.

Tin melts at a low temperature of about 232 °C (450 °F), which is further reduced to <hl> 177.3 °C (351.1 °F) for 11 nm particles <hl> .


Question: What is β-tin's stable temperature?

β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable. In contrast, α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F), is brittle. α-tin has a diamond cubic crystal structure, similar to diamond, silicon or germanium. α-tin has no metallic properties at all because its atoms form a covalent structure where electrons cannot move freely. It is a dull-gray powdery material with no common uses, other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more commonly known as gray tin and white tin, respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F)  and pressures above several GPa. In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". Although the α-β transformation temperature is nominally 13.2 °C (55.8 °F), impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C (32 °F) and, on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin.

Answer: β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable.

<hl> β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable. In contrast, α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F), is brittle. <hl> α-tin has a diamond cubic crystal structure, similar to diamond, silicon or germanium. α-tin has no metallic properties at all because its atoms form a covalent structure where electrons cannot move freely. It is a dull-gray powdery material with no common uses, other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more commonly known as gray tin and white tin, respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F) and pressures above several GPa. In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". Although the α-β transformation temperature is nominally 13.2 °C (55.8 °F), impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C (32 °F) and, on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin.

<hl> β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable. <hl> In contrast, α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F), is brittle. α-tin has a diamond cubic crystal structure, similar to diamond, silicon or germanium. α-tin has no metallic properties at all because its atoms form a covalent structure where electrons cannot move freely. It is a dull-gray powdery material with no common uses, other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more commonly known as gray tin and white tin, respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F) and pressures above several GPa. In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". Although the α-β transformation temperature is nominally 13.2 °C (55.8 °F), impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C (32 °F) and, on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin.


Question: What is α-tin's stable temperature?

Answer: α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F)

β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable. <hl> In contrast, α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F) , is brittle. <hl> α-tin has a diamond cubic crystal structure, similar to diamond, silicon or germanium. α-tin has no metallic properties at all because its atoms form a covalent structure where electrons cannot move freely. It is a dull-gray powdery material with no common uses, other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more commonly known as gray tin and white tin, respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F) and pressures above several GPa. In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". Although the α-β transformation temperature is nominally 13.2 °C (55.8 °F), impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C (32 °F) and, on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin.

β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable. In contrast, <hl> α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F) <hl>, is brittle. α-tin has a diamond cubic crystal structure, similar to diamond, silicon or germanium. α-tin has no metallic properties at all because its atoms form a covalent structure where electrons cannot move freely. It is a dull-gray powdery material with no common uses, other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more commonly known as gray tin and white tin, respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F) and pressures above several GPa. In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". Although the α-β transformation temperature is nominally 13.2 °C (55.8 °F), impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C (32 °F) and, on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin.

In contrast, <hl> α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F) <hl> , is brittle.


Question: Are there any more allotropes?

Answer: Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F)  and pressures above several GPa

β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable. In contrast, α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F), is brittle. α-tin has a diamond cubic crystal structure, similar to diamond, silicon or germanium. α-tin has no metallic properties at all because its atoms form a covalent structure where electrons cannot move freely. It is a dull-gray powdery material with no common uses, other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more commonly known as gray tin and white tin, respectively. <hl> Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F) and pressures above several GPa . <hl> In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". Although the α-β transformation temperature is nominally 13.2 °C (55.8 °F), impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C (32 °F) and, on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin.

β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable. In contrast, α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F), is brittle. α-tin has a diamond cubic crystal structure, similar to diamond, silicon or germanium. α-tin has no metallic properties at all because its atoms form a covalent structure where electrons cannot move freely. It is a dull-gray powdery material with no common uses, other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more commonly known as gray tin and white tin, respectively. <hl> Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F) and pressures above several GPa <hl>. In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". Although the α-β transformation temperature is nominally 13.2 °C (55.8 °F), impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C (32 °F) and, on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin.

<hl> Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F) and pressures above several GPa <hl> .


Question: Can "tin pest" not happen?

Answer: on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin.

β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable. In contrast, α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F), is brittle. α-tin has a diamond cubic crystal structure, similar to diamond, silicon or germanium. α-tin has no metallic properties at all because its atoms form a covalent structure where electrons cannot move freely. It is a dull-gray powdery material with no common uses, other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more commonly known as gray tin and white tin, respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F) and pressures above several GPa. In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". Although the α-β transformation temperature is nominally 13.2 °C (55.8 °F), impurities (e.g. Al, Zn, etc.) <hl> lower the transition temperature well below 0 °C (32 °F) and, on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin. <hl>

β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable. In contrast, α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F), is brittle. α-tin has a diamond cubic crystal structure, similar to diamond, silicon or germanium. α-tin has no metallic properties at all because its atoms form a covalent structure where electrons cannot move freely. It is a dull-gray powdery material with no common uses, other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more commonly known as gray tin and white tin, respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F) and pressures above several GPa. In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". Although the α-β transformation temperature is nominally 13.2 °C (55.8 °F), impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C (32 °F) and, <hl> on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin. <hl>


Question: What happens to β-tin at cold temperatures?

Answer: In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest".

β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable. In contrast, α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F), is brittle. α-tin has a diamond cubic crystal structure, similar to diamond, silicon or germanium. α-tin has no metallic properties at all because its atoms form a covalent structure where electrons cannot move freely. It is a dull-gray powdery material with no common uses, other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more commonly known as gray tin and white tin, respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F) and pressures above several GPa. <hl> In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". Although the α-β transformation temperature is nominally 13.2 °C (55.8 °F), impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C (32 °F) and, on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin. <hl>

β-tin (the metallic form, or white tin), which is stable at and above room temperature, is malleable. In contrast, α-tin (nonmetallic form, or gray tin), which is stable below 13.2 °C (55.8 °F), is brittle. α-tin has a diamond cubic crystal structure, similar to diamond, silicon or germanium. α-tin has no metallic properties at all because its atoms form a covalent structure where electrons cannot move freely. It is a dull-gray powdery material with no common uses, other than a few specialized semiconductor applications. These two allotropes, α-tin and β-tin, are more commonly known as gray tin and white tin, respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C (322 °F) and pressures above several GPa. <hl> In cold conditions, β-tin tends to transform spontaneously into α-tin, a phenomenon known as "tin pest". <hl> Although the α-β transformation temperature is nominally 13.2 °C (55.8 °F), impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C (32 °F) and, on the addition of Sb or Bi, the transformation may not occur at all, increasing the durability of the tin.


Question: Why does tin resist transformation?

Commercial grades of tin (99.8%) resist transformation because of the inhibiting effect of the small amounts of bismuth, antimony, lead and silver present as impurities. Alloying elements such as copper, antimony, bismuth, cadmium and silver increase its hardness. Tin tends rather easily to form hard, brittle intermetallic phases, which are often undesirable. It does not form wide solid solution ranges in other metals in general, and there are few elements that have appreciable solid solubility in tin. Simple eutectic systems, however, occur with bismuth, gallium, lead, thallium and zinc.

Answer: because of the inhibiting effect of the small amounts of bismuth, antimony, lead and silver present as impurities.

<hl> Commercial grades of tin (99.8%) resist transformation because of the inhibiting effect of the small amounts of bismuth, antimony, lead and silver present as impurities. Alloying elements such as copper, antimony, bismuth, cadmium and silver increase its hardness. <hl> Tin tends rather easily to form hard, brittle intermetallic phases, which are often undesirable. It does not form wide solid solution ranges in other metals in general, and there are few elements that have appreciable solid solubility in tin. Simple eutectic systems, however, occur with bismuth, gallium, lead, thallium and zinc.

Commercial grades of tin (99.8%) resist transformation <hl> because of the inhibiting effect of the small amounts of bismuth, antimony, lead and silver present as impurities. <hl> Alloying elements such as copper, antimony, bismuth, cadmium and silver increase its hardness. Tin tends rather easily to form hard, brittle intermetallic phases, which are often undesirable. It does not form wide solid solution ranges in other metals in general, and there are few elements that have appreciable solid solubility in tin. Simple eutectic systems, however, occur with bismuth, gallium, lead, thallium and zinc.


Question: What happens to tin?

Answer: Tin tends rather easily to form hard, brittle intermetallic phases, which are often undesirable.

Commercial grades of tin (99.8%) resist transformation because of the inhibiting effect of the small amounts of bismuth, antimony, lead and silver present as impurities. Alloying elements such as copper, antimony, bismuth, cadmium and silver increase its hardness. <hl> Tin tends rather easily to form hard, brittle intermetallic phases, which are often undesirable. It does not form wide solid solution ranges in other metals in general, and there are few elements that have appreciable solid solubility in tin. <hl> Simple eutectic systems, however, occur with bismuth, gallium, lead, thallium and zinc.

Commercial grades of tin (99.8%) resist transformation because of the inhibiting effect of the small amounts of bismuth, antimony, lead and silver present as impurities. Alloying elements such as copper, antimony, bismuth, cadmium and silver increase its hardness. <hl> Tin tends rather easily to form hard, brittle intermetallic phases, which are often undesirable. <hl> It does not form wide solid solution ranges in other metals in general, and there are few elements that have appreciable solid solubility in tin. Simple eutectic systems, however, occur with bismuth, gallium, lead, thallium and zinc.


Question: Which elements increase tin's hardness?

Answer: copper, antimony, bismuth, cadmium and silver increase its hardness.

Commercial grades of tin (99.8%) resist transformation because of the inhibiting effect of the small amounts of bismuth, antimony, lead and silver present as impurities. <hl> Alloying elements such as copper, antimony, bismuth, cadmium and silver increase its hardness. Tin tends rather easily to form hard, brittle intermetallic phases, which are often undesirable. <hl> It does not form wide solid solution ranges in other metals in general, and there are few elements that have appreciable solid solubility in tin. Simple eutectic systems, however, occur with bismuth, gallium, lead, thallium and zinc.

Commercial grades of tin (99.8%) resist transformation because of the inhibiting effect of the small amounts of bismuth, antimony, lead and silver present as impurities. Alloying elements such as <hl> copper, antimony, bismuth, cadmium and silver increase its hardness. <hl> Tin tends rather easily to form hard, brittle intermetallic phases, which are often undesirable. It does not form wide solid solution ranges in other metals in general, and there are few elements that have appreciable solid solubility in tin. Simple eutectic systems, however, occur with bismuth, gallium, lead, thallium and zinc.


Question: Can eutectic systems occur?

Answer: Simple eutectic systems, however, occur with bismuth, gallium, lead, thallium and zinc.

Commercial grades of tin (99.8%) resist transformation because of the inhibiting effect of the small amounts of bismuth, antimony, lead and silver present as impurities. Alloying elements such as copper, antimony, bismuth, cadmium and silver increase its hardness. Tin tends rather easily to form hard, brittle intermetallic phases, which are often undesirable. It does not form wide solid solution ranges in other metals in general, and there are few elements that have appreciable solid solubility in tin. <hl> Simple eutectic systems, however, occur with bismuth, gallium, lead, thallium and zinc. <hl>


Question: What is the name of  the superconductor that is below 3.72K?

Tin becomes a superconductor below 3.72 K. In fact, tin was one of the first superconductors to be studied; the Meissner effect, one of the characteristic features of superconductors, was first discovered in superconducting tin crystals.

Answer: Tin

<hl> Tin becomes a superconductor below 3.72 K. <hl> In fact, tin was one of the first superconductors to be studied; the Meissner effect, one of the characteristic features of superconductors, was first discovered in superconducting tin crystals.

<hl> Tin <hl> becomes a superconductor below 3.72 K. In fact, tin was one of the first superconductors to be studied; the Meissner effect, one of the characteristic features of superconductors, was first discovered in superconducting tin crystals.


Question: Tin is the first superconductors to do what?

Answer: to be studied

Tin becomes a superconductor below 3.72 K. <hl> In fact, tin was one of the first superconductors to be studied ; the Meissner effect, one of the characteristic features of superconductors, was first discovered in superconducting tin crystals. <hl>

Tin becomes a superconductor below 3.72 K. In fact, tin was one of the first superconductors <hl> to be studied <hl>; the Meissner effect, one of the characteristic features of superconductors, was first discovered in superconducting tin crystals.

In fact, tin was one of the first superconductors <hl> to be studied <hl> ; the Meissner effect, one of the characteristic features of superconductors, was first discovered in superconducting tin crystals.


Question: Name one of the characteristic  features of superconductors.

Answer: the Meissner effect

Tin becomes a superconductor below 3.72 K. <hl> In fact, tin was one of the first superconductors to be studied; the Meissner effect , one of the characteristic features of superconductors, was first discovered in superconducting tin crystals. <hl>

Tin becomes a superconductor below 3.72 K. In fact, tin was one of the first superconductors to be studied; <hl> the Meissner effect <hl>, one of the characteristic features of superconductors, was first discovered in superconducting tin crystals.

In fact, tin was one of the first superconductors to be studied; <hl> the Meissner effect <hl> , one of the characteristic features of superconductors, was first discovered in superconducting tin crystals.


Question: Where was the Meissner effect first discovered?

Answer: tin crystals

Tin becomes a superconductor below 3.72 K. <hl> In fact, tin was one of the first superconductors to be studied; the Meissner effect, one of the characteristic features of superconductors, was first discovered in superconducting tin crystals . <hl>

Tin becomes a superconductor below 3.72 K. In fact, tin was one of the first superconductors to be studied; the Meissner effect, one of the characteristic features of superconductors, was first discovered in superconducting <hl> tin crystals <hl>.

In fact, tin was one of the first superconductors to be studied; the Meissner effect, one of the characteristic features of superconductors, was first discovered in superconducting <hl> tin crystals <hl> .


Question: What is Tin known to resits?

Tin resists corrosion from water, but can be attacked by acids and alkalis. Tin can be highly polished and is used as a protective coat for other metals. In this case a protective oxide layer prevents further oxidation. This oxide layer forms on pewter and other tin alloys. Tin acts as a catalyst when oxygen is in solution and helps accelerate chemical attack.[clarification needed][citation needed]

Answer: corrosion from water

<hl> Tin resists corrosion from water , but can be attacked by acids and alkalis. <hl> Tin can be highly polished and is used as a protective coat for other metals. In this case a protective oxide layer prevents further oxidation. This oxide layer forms on pewter and other tin alloys. Tin acts as a catalyst when oxygen is in solution and helps accelerate chemical attack.[clarification needed][citation needed]

Tin resists <hl> corrosion from water <hl>, but can be attacked by acids and alkalis. Tin can be highly polished and is used as a protective coat for other metals. In this case a protective oxide layer prevents further oxidation. This oxide layer forms on pewter and other tin alloys. Tin acts as a catalyst when oxygen is in solution and helps accelerate chemical attack.[clarification needed][citation needed]

Tin resists <hl> corrosion from water <hl> , but can be attacked by acids and alkalis.


Question: What elements can Tin be attacked by?

Answer: acids and alkalis

<hl> Tin resists corrosion from water, but can be attacked by acids and alkalis . <hl> Tin can be highly polished and is used as a protective coat for other metals. In this case a protective oxide layer prevents further oxidation. This oxide layer forms on pewter and other tin alloys. Tin acts as a catalyst when oxygen is in solution and helps accelerate chemical attack.[clarification needed][citation needed]

Tin resists corrosion from water, but can be attacked by <hl> acids and alkalis <hl>. Tin can be highly polished and is used as a protective coat for other metals. In this case a protective oxide layer prevents further oxidation. This oxide layer forms on pewter and other tin alloys. Tin acts as a catalyst when oxygen is in solution and helps accelerate chemical attack.[clarification needed][citation needed]

Tin resists corrosion from water, but can be attacked by <hl> acids and alkalis <hl> .


Question: What can Tin be use for?

Answer: protective coat

Tin resists corrosion from water, but can be attacked by acids and alkalis. <hl> Tin can be highly polished and is used as a protective coat for other metals. <hl> In this case a protective oxide layer prevents further oxidation. This oxide layer forms on pewter and other tin alloys. Tin acts as a catalyst when oxygen is in solution and helps accelerate chemical attack.[clarification needed][citation needed]

Tin resists corrosion from water, but can be attacked by acids and alkalis. Tin can be highly polished and is used as a <hl> protective coat <hl> for other metals. In this case a protective oxide layer prevents further oxidation. This oxide layer forms on pewter and other tin alloys. Tin acts as a catalyst when oxygen is in solution and helps accelerate chemical attack.[clarification needed][citation needed]