Assertion: circle's area | /r/HasProperty | equal
Facets:
value: to that of a right triangle
type: OTHER
value: to π
type: OTHER
value: to the integral
type: OTHER
value: to the surface of a plane
type: LOCATION
value: to 2 ⋅
type: OTHER
value: to 2
type: OTHER
value: inside a circle
type: LOCATION
value: to the radius
type: OTHER
value: exactly
type: DEGREE
value: in his measurement of a circle
type: OTHER
Source sentences:
text: As proved by Archimedes, in his Measurement of a Circle, the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, which comes to π multiplied by the radius squared:
text: The area of the circle is equal to π times the area of the gray square.
text: The area, a, inside a circle is equal to the radius multiplied by itself, then multiplied by π (a equals π times r times r).
text: Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius in his book Measurement of a Circle.
text: The area of each of these triangles is equal to 1 / 2 ⋅ r ⋅
text: So the divergence of r is equal to two, and hence the area of a disc D is equal to
text: The integral of ds over the whole circle ∂ D {\displaystyle \partial D} is just the arc length, which is its circumference, so this shows that the area A enclosed by the circle is equal to R / 2 {\displaystyle R/2} times the circumference of the circle.
text: Therefore, the area of a circle of radius r, which is twice the area of the semi-circle, is equal to 2 ⋅ π
text: In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized Squaring the circle: the areas of this square and this circle are both equal to.
text: Its area is equal to the area of the triangle(found by Hippocrates of Chios ).
text: In other words, it is impossible to construct, using compass and straightedge alone, a square whose area is exactly equal to the area of a given circle.
text: which says that the area under the basic bell curve in the figure is equal to the square root of π.
text: The mathematician Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, in his book Measurement of a Circle.
text: The area between the graphs of two functions is equal to the integral of one function, f(x), minus the integral of the other function, g(x):
text: Area of a circle is equal to the surface of a plane that is limited by a circle.