mathematical views

Ayelet Lindenstrauss Larsen

TDP Gallery | August 28 – October 3, 2020

This work consists of snapshots of images I came across as a mathematician which appealed to me visually. Like photos of favorite views of the countryside, but made in fiber. Many of these images are of ideas rather than of things which are physically there, so they first have to be realized.

Two of the images are of perfect squares. It is easy to divide a square into smaller squares, but much harder if you insist that no two of those smaller squares have the same size. I was surprised to learn that it was even possible to find such a decomposition, but loved the elegant interlocking of the squares in the solutions once I saw them. In 1978, A. J. W. Duivestijn found a way of decomposing a square into 21 smaller squares of different sizes, and showed that you cannot do it with fewer squares. I embroidered his solution as well as an earlier solution, due to T. H. Willcocks, which involves 24 small squares but has the added feature of an internal rectangle composed of some of the smaller squares.

A hyperbolic plane is a kind of two-dimensional surface where if you pick any point and start looking at concentric circles around it, their circumferences grow more quickly than in the plane. There is enough “extra” that around any point, the surface can be turned and bent (without stretching) to resemble a mountain pass between two peaks. It turns out that probably the easiest low-tech way of producing a piece of a hyperbolic plane is crochet: you keep increasing stitches at a fixed rate and never stop. The resulting exponential growth leads to wild ruffles and curls, and gives the surface power which reads as big even when the surface itself is small. Constructing little rooms around the hyperbolic surfaces gives them surroundings that they can interact with. I always add a small chair, from which the surface can be properly contemplated.

The least mathematical, but also the most immediately relevant to my personal math- ematical life, are the notebook pages. I like the way a handwritten page of mathematics looks. And nevertheless (actually, because of that) I doodle on many of mine. In order to concentrate better as I’m thinking. Or in frustration, when I am not making progress on a problem. Or in even more frustration, in order to cross out things I had written which I have since realized were wrong. “Re-Use” is similar to the other notebook pages, but the embroidery on it is completely independent of the mathematical writing. As a child growing up, our drawing paper was the backs of my father’s old typed mathematics drafts, and this piece is about the memory of that paper with math on it as the starting point for artistic efforts.