Mathematical Quilts

Some of my work...


The Sum of Odd Integers - The inspiration for this quilt began with an image found in
Roger B. Nelsen's book Proof Without Words--Exercises in Visual Thinking. 
The quilt has 4 congruent triangular sections.  The side length of the square is 2n,
and the last odd integer may be expressed by 2n-1.  To find the sum of odd integers
we add 1 + 3 + ...+(2n-1) = 1/4(2n)(2n)= n squared.  The quilt was hand quilted with the 17 symmetry group patterns.

DaVinci’s Dessert -
Sherbert Without Pi—When Leonardo DaVinci became interested
in dissections, it is thought he was trying to square the circle. Today we know that
this is impossible. In this quilt, the curvilinear gold shapes can be cut and put together
to form a rectangle. Leonardo’s solution was elegant and unusual.
A short video of this quilt can be found here.

Leonardo’s Treat -
This quilt was based on a design in Herbert Wills III book -
Leonardo’s Dessert—No Pi. A delightful pattern that nests squares and circles. This pattern
is found on floors around the world. Many interesting area relationships can be found in this pattern.
The quilt is in a private collection.

San Gaku -
The San Gaku tablets come from Japan during the Edo period—1603-1867.
The tablets number around 800, and are found in various shrines in Japan. These
San Gaku were found in the Kono Hachimen Shrine outside Tokyo. Solving a San Gaku
was a way of venerating the Gods.

Sierpinkskis Triangle -
Waclaw Sierpinski, 1882-1969, was a Polish mathematician that
was very interested in patterns, including Pythagorean triples. This triangle, a fractal,
was found on the floor of a church in Anagni, Italy. This oldest fractal dates to 1104. It is
said that this fractal, named after Sierpinski, is the first fractal in the fractal alphabet. The
quilt is owned by the London Science Museum.

Pascal’s Surprise -

A quilt made for Marc Roth based on Blaise Pascal’s (1623-1662)
number pattern. The Pascal triangle was actually found in literature as early as 1303 by
Cho Ski-kie. The pattern formed here is found by taking Pascal’s triangle and inserting
a new triangle in between existing numbers. The colors reflect if the number is even or odd.


The Droste Effect - The inspiration of this quilt came from an article by Jos Leys in 2008.
The article entitled "Behind the Droste Effect" detailed the mathematics behind the image
created by M.C. Escher in his 1956 drawing "Print Gallery". The logarithmic image transformation method was analyzed by professor Hendrik Lenstra at Leiden University. Transformation, rotation, scaling and exponentiation are used in this process. The Bird of Paradise flower was repeated in this particular transformation.


    Bead Necklace:  Universal Cycle - The loop around the outside of the quilt is comprised of 8 colors, 7 of each, so that each of the 56 combinations of 3 colors occurs exactly once in 3 consecutive rectangles. 
This is an example of a universal cycle promoted by Ron Graham and Persi Diaconis.  It was constructed by hooking together the 14 squares and traveling around the outside of the structure (an Euler Tour). 
The 4 colors of each square can be separated onto 4 unique triples of colors.  The 14 squares together
make up a Steiner quadruple system.  The rectangle separated into 14 triangles is the smallest
triangulation of the torus, and yields a Fano plane.  This particular solution was found by Marc Roth in
1985 and is an alternative construction to the one found by Brad Jackson.    


Some quilts are for sale - please contact Elaine at for more
information and prices.