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What is Coordinate Paper?

By C.B. Fox
Updated May 21, 2024
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Coordinate paper, also called graph paper, is a type of paper that has been printed with lines that make up a grid system. These grids can be arranged in a number of different ways, including in Cartesian, polar and logarithmic coordinate systems. Many industries make use of coordinate paper, including engineering, architecture and business. Graph paper is especially useful for plotting a visual representation of mathematical data and for scaling designs.

The most common type of coordinate paper is paper printed with a simple, equally spaced grid. This is called the Cartesian coordinate system and was developed by Rene Descartes, a mathematician and philosopher of the seventeenth century. By isolating two separate directions, one along a horizontal, or X-axis, and one along a vertical, or Y-axis, Cartesian coordinates can be used to pinpoint locations on a map or a graph. The center of one of these graphs is given the location (0,0) and from there, direction along either the X or Y axis can be measured in either positive or negative numbers.

Another type of coordinate paper, which is often used in calculus, is polar coordinate paper. In this system, coordinates are measured by a point’s distance away from the fixed center of the coordinate system, or the origin, and the measure of the angle formed by drawing a ray between the origin and the point. This system is particularly useful when studying curves and spirals. It is also possible to study curves with bilateral symmetry on a bipolar system, in which there are two fixed points, or focuses.

In logarithmic coordinate paper, lines are drawn on a grid similarly to the Cartesian coordinate system. The difference in logarithmic paper is that the distance between the lines is not the same in each case, but is defined through a mathematical function called a logarithm. Though there are many logarithms used to create these grids, one of the most common is one in which the distance between these lines decreases by half for consecutive each line.

All of these types of coordinate paper are most commonly used in industries that deal with mathematical data, including engineering, architecture and business. In these industries, it is often helpful to create visual representations of numerical data, in the form of graphs, which gives coordinate paper its other name, graph paper. Coordinate paper can also be used in art when breaking up a large picture into small components. This is particularly useful when scaling images.

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