Approximations of π
memorization as approximation

Evan Daniel: Approximations
TWO APPROXIMATIONS OF π | 2014 | 56" * 64" | Oil on canvas, π written from memory to 3,584 digits.
The canvas size of 4 2/3 feet was chosen to allow the repeating fraction to form vertical lines of alternating colors.
Evan Daniel: Approximations
DETAIL OF TWO APPROXIMATIONS OF π
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.
Evan Daniel: Approximations
DEEP π 2014 | 22" * 26" | oil on canvas, π mapped from memory to 800 digits.
THREE APPROXIMATIONS OF π | 2015 | 64" * 3" | Aluminum bar (CNC fabricated), projection.
In this iteration the projected colors are algorithmically generated.
Evan Daniel: Approximations
In this case, the deductive approximation of π is 22/7, which repeats inverts after three digits and repeats after six, leading to a width of three inches.
Evan Daniel: Approximations
The depth of the blocks varies by slightly less than an inch, and represents the digits beginning where TWO APPROXIMATIONS OF π ends.
Evan Daniel: Approximations
THREE APPROXIMATIONS OF π (PAINTED VERSION) | 2016 | 64" * 3" | Aluminum bar (CNC fabricated), oil and oil primer. In this iteration the colors are painted over the aluminum.


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.

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