A multi-axis educational graphing ruler is described. The ruler includes: a first set of markings placed such that the markings extend vertically if the ruler is placed in a first orientation; and a second set of markings oriented such that the markings extend horizontally if the ruler is placed in a second orientation that is perpendicular to the first orientation. A ruler includes: a first set of markings and labels associated with a first axis; and a second set of markings and labels associated with a second axis that is perpendicular to the first axis. A plotting tool includes: a first set of markings and labels along a first surface of the tool; and a second set of markings and labels along a second surface of the tool, wherein the second surface is perpendicular to the first surface.

DETAILED DESCRIPTION OF THE INVENTION

Various inventive features are described below that can each be used independently of one another or in combination with other features. Broadly, some embodiments of the present invention generally provide a multi-axis educational graphing ruler.

FIG. 1illustrates front views of a graphing ruler100according to an exemplary embodiment the invention. Such rulers may have varying lengths, widths, and/or thicknesses, as appropriate. The ruler may be made of various appropriate materials (e.g., plastic, metal, wood, etc.). In some embodiments, the ruler may be at least partially transparent such that elements associated with a graphing medium (e.g., gridlines, previously plotted points, etc.) may be visible while the ruler is being used.

The size, shape, and/or other attributes of the ruler may be based at least partly on various attributes of the user and/or other appropriate factors (e.g., materials used, size of graphical elements, desired grid spacing, etc.). For instance, the rulers may have varying attributes based on intended age, education level, mathematic aptitude, etc. of the user or users. In one example embodiment, the rule may be approximately seven inches long, approximately one-and-a-half inches wide, and approximately one thirty-second of an inch thick.

As shown, in a first orientation110, the ruler100may be aligned such that a first set of markings120(and associated labels), corresponding to points along an “X” axis, is placed in an upright position. Likewise, in a second orientation130, the ruler may be aligned such that a second set of markings140(and associated labels), corresponding to points along a “Y” axis, is placed in an upright position. As shown, in some embodiments each set of markings may be centered on a value of zero and extend in positive and negative directions (with associated positive and negative labels). Each marking may be associated with a particular label.

The first set of markings may have a first spacing150and the second set of markings may have a second spacing160. In the example ofFIG. 1, the markings120and140are evenly spaced and uniform across the two axes. The spacing between the markings along each axis may correspond to grid spacing provided by various types of graph paper and/or other mediums (e.g., one-quarter inch spacing between markings for use with standard graph paper). One of ordinary skill in the art will recognize that the markings may be spaced at uneven intervals and may be non-uniform across the axes. The markings may correspond to various appropriate coordinate systems (e.g., Cartesian coordinate system, polar coordinate system, cylindrical and spherical coordinate systems, etc.).

For instance, some embodiments may utilize spacings associated with a trigonometric scale that is based on various values along a unit circle. Such scales may be used to plot functions such as sin functions, cosine functions, and/or other trigonometric functions, as appropriate. As another example, some scales may be adapted to be used to plot logarithmic functions. As yet another example, some scales may be used to plot calculus functions. Various other scales may be associated with various other functions (e.g., exponential functions, normal distributions, etc.).

Some embodiments may include various other labels or graphic elements170, at various appropriate locations on the ruler. For instance, a first axis may be labeled in one or more appropriate ways (e.g., “X”, “run”, “ΔX”, “x-axis”, etc.). As another example, a second axis may be labeled in one or more appropriate ways (e.g., “Y”, “rise”, “ΔY”, “y-axis”, etc.). Some embodiments may include a center point indicator such as a circle with perpendicular lines located at the center of the ruler. Some embodiments may include equations, instructions, notes, etc. (e.g., “slope=rise/run=ΔY/ΔX”, “(X,Y)”, etc.).

Some embodiments may be adapted to be used by students when plotting ordered pairs (i.e., points defined by a pair of integers representing an x-coordinate and a y-coordinate in a Cartesian coordinate system). The center of the ruler100may allow students to align the ruler with a center on a plot area. A student may then place the ruler in a first orientation to determine the appropriate gridline associated with an x-coordinate and may then place the ruler in a second orientation to determine the appropriate gridline associated with the y-coordinate and plot the point associated with the pair of coordinates.

In some embodiments, the ruler may include various through-holes, notches, etc., that may allow a user to easily mark a point along an axis, the secure the ruler to a plot medium, etc.

FIG. 2illustrates front, side, and top views of an alternative graphing ruler200according to an exemplary embodiment of the invention. In this example, a first set of markings is placed along a first surface of the ruler200, while a second set of markings is placed along a second surface perpendicular to the first surface. To change from the first orientation210to the second orientation220, the ruler may be rotated ninety degrees counterclockwise about a first axis and then turned ninety degrees counterclockwise about a second, perpendicular axis to display the second surface. Such a ruler may generally be shaped similarly to a rectangular pencil (e.g., a typical carpenter's pencil), and may include graphite or some other appropriate material such that the ruler may be used to mark various mediums.

Different embodiments may be adapted to use different types of materials (e.g., graphite, ink, etc.) to mark different types of mediums (e.g., paper, wood, etc.). In addition, some embodiments may include markings that are associated with construction or other specific uses (e.g., by facilitating plotting of forty-five degree angles).

Although the examples described above have used two axes, one of ordinary skill in the art will recognize that some embodiments may include more than two axes (e.g., a three-axis ruler). Such a three-axis ruler may include a first element that is substantially similar to the ruler100described above in reference toFIG. 1and a second element that extends along a third axis (e.g., a “Z” axis) and that may be connected to, or otherwise position in relation to, the first element such that a value along the third axis may be determined.

It should be understood, of course, that the foregoing relates to illustrative details of exemplary embodiments of the invention and that modifications may be made without departing from the spirit and scope of the invention as defined by the following claims.