# Medieval Math, Khayyam-Pascal

## Medieval Math, Khayyam-Pascal, 2015

In the ** Khayyam-Pascal** installation, 2015-2016, I screen-printed layers of mathematical diagrams and binomial coefficient (numbers), Khayyam’s mathematics manuscript page, and Sierpiński’s triangle patterns on 160-360 hand-cut felt triangles. The pyramid pattern of the installation resembles Pascal Triangle. In mathematics, the Pascal triangle is a triangular array of binomial coefficients. It is named after the 17th-century French mathematician, Blaise Pascal. However, the 12th-century Iranian mathematician, Khayyam, had studied it centuries before Pascal. Through this installation, I pay homage to both mathematicians.

*Khayyam-Pascal, *2015, silkscreen on 160 hand-cut felt triangles and magnets, 10 x 4 feet

InSpace Curatorial Gallery, San Francisco, CA

(The gallery is in Pacific Felt Factory building which was a formerly a felt factor in the San Francisco Mission that was renovated into a gallery and studio spaces for artists)

*Khayyam-Pascal, *2015, silkscreen on hand-cut felt triangles and magnets, 10 x 4 feet

*Khayyam-Pascal, *2015, silkscreen on 160 hand-cut felt triangles and magnets, 10 x 4 feet

*Khayyam-Pascal, *MIT, Rotch Library, 2018

*Khayyam-Pascal*, 2016, silkscreen on 360 hand-cut felt triangles, 7 x 16 feet, California State University, Stanislaus

*Khayyam-Pascal*, 2016, California State University, Stanislaus

*Khayyam-Pascal*, 2016, laser-etched wood triangles and screws, mock-up for a permanent installation, 69″x 40″

## Research

Blaise Pascal’s version of the triangle Rows zero to five of Pascal’s triangle

“The rows of Pascal’s triangle are conventionally enumerated starting with row *n* = 0 at the top (the 0th row). The entries in each row are numbered from the left beginning with *k* = 0 and are usually staggered relative to the numbers in the adjacent rows. The triangle may be constructed in the following manner: In row 0 (the topmost row), there is a unique nonzero entry 1. Each entry of each subsequent row is constructed by adding the number above and to the left with the number above and to the right, treating blank entries as 0. For example, the initial number in the first (or any other) row is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.”

The pattern obtained by coloring only the odd numbers in Pascal’s triangle closely resembles the fractal called the Sierpinski triangle