# Graph Paper

Here is a collection of graph paper of various sorts, all downloadable in pdf format. It is possible that the screen images of certain graph paper will give the appearance that some lines are thicker (or darker) than others. That is the case with several such as polar and semi-log, but for the Cartesian paper all lines should print with equal thickness.

## Cartesian (Square Grid) Paper

Five lines per inch

Four lines per inch

Three lines per inch

Two lines per inch

Legal size (8 1/2" X 14") -- Excellent for trigonometric function graphs.

## Polar Graph Paper

Polar graph paper is used for polar coordinates, which consist of a radial distance r from the origin and a rotation of an angle of theta degrees or radians counter-clockwise from the polar axis (positive x axis).

Large single polar graph --Thirty scale marks for r in increments of five degrees.

Smaller (double) polar graph -- Two polar graphs on one page, each with twenty scale marks for r in increments of five degrees.

Combined Cartesian and Polar -- There are three pages here. One is a large Cartesian grid, one a large polar grid, and the third has one superimposed on the other. These were created for overhead projector transparencies for introducing the polar coordinate system in class, and are in two colors.

## Semi-Log Graph Paper

Semi-log graph paper is useful for graphing certain kinds of data in science or engineering. In particular, exponential growth or decay data will appear linear on this coordinate system. I use two sheets in classes to illustrate addition of logarithms as a demonstration of the principle behind slide rules.

Semi-log scaled -- The horizontal axis has evenly spaced scale markings from 0 to 10. The vertical axis has three orders of magnitude, marked from 1 to 1000.

Semi-log unscaled -- Same as above but with all numbers removed.

## Unusual Graph Paper

Cardioid paper -- This one-of-a-kind and otherwise useless graph paper was inspired by two former Math 290 students who wondered if they could create a unique coordinate system and do calculus using cardioids--heart shaped graphs. They succeeded in creating their coordinate system, found the Jacobian and managed a couple integrations. I helped them out by creating this paper and a good laugh was enjoyed by all! These cardioids have the polar coordinate form r = a [1 + cos (theta) ].

All graph paper is copyright © 2004 by Jon Davidson. Any of these graph papers may be reprinted or copied without permission, but may not be resold. For suggestions or comments please contact the author: Jon Davidson.