Lutes of Pythagoras - Pythagoras was born on the island of Samos in 570 B.C. His extensive
work with music is probably why the long shaped objects in this quilt are called lutes. A lute
is a musical instrument. The lute has the golden ratio (1 to 1.618) proportion in a variety of
places. Many interesting things happened while designing this quilt. The use of the exterior
angle theorem was used. The delightful quilting lines in the negative spaces made
interesting patterns that were a surprise!

Spiraling Pythagorean Triples - case 1 - This quilt belongs to the London Science Museum.
The fabrics were hand-dyed to create the 3-4-5 triangle, the 5-12-13 triangle, the 7-24-25
triangle, and the 9-40-41 triangle. In this version of the triangles, the triangles are
reflected on their hypotenuse.





Spiraling Pythagorean Triples - case 2 - This quilt has the same triangles as
the case 1 quilt. The difference being that the triangles are rotated about their
hypotenuse, rather than reflected. The quilt is made with three-quarter inch squares
which became difficult to handle at the 9-40-41 size.






The Wheel of Theodorus - Theodorus of Cyrene participated in the Cyrenaic school
of moral philosophy. He tutored Plato and was a Pythagorean. His lifetime spans
465 to 398 B.C. During this time period the Greeks just started using written numerals.
Further, the concept of the irrational number developed around this time. This quilt starts
with an isosceles right triangle with sides 1, 1, and the square root of 2.






The Six Trigonometric Functions - The history of trigonometry goes back to the earliest
recorded mathematics in Egypt and Babylon. In the 2nd century B.C., the astronomer
Hipparchus compiled a trigonometric table for solving triangles. Since then many nationalities
have contributed to the development of this subject: Indians, Muslims, Germans, Scottish,
Swiss, Arabic, etc. The sine, cosine, tangent, cosecant, secant, and cotangent are
represented here. The tiles surrounding the quilt are Moorish tiles from the Alcazar. This quilt is owned in a private collection.





The Sacred Cut - Mosaics and paintings in the Garden Houses of Ostia are in many
cases laid out according to the geometry of the sacred cut. The sacred cut is comprised
of three squares, two Roman rectangles of proportion square root of two:1,
and two Roman rectangles of the proportion sqaure root of two plus 1 : 1. 
The very center of this quilt begins the construction of the sacred cut--parallel
lines must be added to complete the proportions for the rectangles.
   

Five Means

     
Behold! Buttons - Andrei Nikolaevich Kolmogorov, born in 1903, is considered by some
to be the greatest Russian mathematician of the twentieth century. Kolmogorov devised the following problem at the age of five:  how many different patterns can you create with
thread while sewing on a four-hole button? This problem appeared in the
April 2011 "Mathematics Teacher" professional journal.  I thought the problem had great possibilities for a striking quilt based on the 63 different ways a button can be sewn on a shirt.
A short video of this quilt can be found here.

Some quilts are for sale - please contact Elaine at eellisonelaine@gmail.com for more
information and prices.