Margaret Kepner

This work is a modified version of an earlier design – The Eightfold Path. Colors have been added, and the flat 2D print has been deconstructed into a folding book format. The underlying design is a visual presentation of the five non-isomorphic groups of order eight: C8, C2 x C4, C2 x C2 x C2, D4, and Q8. It employs a visual vocabulary derived from a traditional quilt pattern, Drunkard’s Path. Each of the small shapes used in the design is a quarter circle in a square, scaled so that its area equals the square’s residual area. The 36-page book structure is created from a single sheet of paper through a series of cuts and folds. A continuous meander folding path is followed, with varying length fold-sequences, and no beginning nor end. When it is fully folded up, the book assumes a double-square footprint. A smaller-scale meander path, which would result in a continuous 144-page book, is expressed through color accents.

This accordion-style book presents a “gallery” of six related designs based on binary operation tables: addition, subtraction, multiplication, division, powers, and roots. The tables are generated using modulus 4 arithmetic, with the numbers 1 to 4 represented by isosceles right triangles in four orientations. There are 24 ways that these four shapes can be assigned to the numbers 1 to 4. Each ordering (or permutation) results in a different mini-table of size 4 x 4; these are arranged in a larger composite table for each operation. Most of the triangles are black, but certain ones are colored to indicate the permutation matrix that corresponds to the ordering associated with each mini-table. Common cyclic orderings have been assigned the same color. In the layout of the book, operations are paired with their inverses; for example, addition faces subtraction. The book can be “read” in a sequential page-by-page manner, or can be opened out into a five-pointed star structure.

This piece is a “coil book” consisting of a strip of paper more than 25 feet long, which is coiled up in a round container. The strip contains a string of right triangles representing the integers from 1 to 512. Fine lines on each triangle indicate the structure of the decomposition into prime factors for the corresponding integer. Prime numbers appear as solid triangles, while an integer of the form n = p x q is represented by a triangle divided into two halves, one for each prime. An integer with 3 prime factors is subdivided into thirds, etc. When a prime appears in a decomposition multiple times, horizontal bands indicate the number of times it is used. The parade-of-triangles motif is reminiscent of a traditional quilt design known as Wild Goose Chase. The 512 geese/integers in this book are not fully fleshed out; only the “barebones” of their factoring into primes is indicated. The white lines against black backgrounds suggest x-rays, reinforcing the idea of bones – goose bones.