The canvas size of 4 2/3 feet was chosen to allow the repeating fraction to form vertical lines of alternating colors.

The mapping of memorized number onto shape is based on a standard keyboard number pad, with one is on the lower left and nine on the upper right. The numbers are represented cumulatively (e.g. '8' is an aggregate of 1, 2, . . . 8), with zero represented as -1. A grid was used, and π was marked out from memory beforehand.

In this iteration the projected colors are algorithmically generated.

TWO APPROXIMATIONS OF π puts memory side-by-side with deductive reasoning.

π (as always, from memory) is represented by the shape of each block of color.

The ratio 355/113, which is an approximation of π (accurate to seven digits), is represented in the color. I "deduced" this value using mental arithmetic. The value of the ratio repeats after 112 digits; since I chose a canvas width of 56 inches, the numbers repeat every two rows, forming vertical bands of color. Each number and the one below it always add up to '9'.

The color each number is mapped to is based on personal interpretation: for example, three feels olive green to me.

The painting is a means of making the formal differences between memory and deduction. The basic differences between a non-repeating number, painted from memory, and a ratio determine the visual qualities of the painting.

THREE APPROXIMATIONS OF π adds a third dimension: a version of π I have deliberately altered to make more aesthetic.