Mathematical Quilts
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
Two Point Perspective - To visualize a two-point perspective, take a box at eye level and turn it so that the corner of the box is towards you. In this perspective, there are two vanishing points at eye level on the horizon line. Notice that the edges of the box running north and south are all parallel, forming a right angle with the horizon line.
Three Point Perspective - A three-point perspective has three vanishing points. To visualize a three-point perspective, turn a box so that you can see a third side to the box---either above you or below you. The three sides of the visible box, when extended infinity far, will locate the vanishing points.
Four Point Perspective - Elizabeth Ahlgrim posed for this four- point perspective quilt. Elizaabeth is playing a Bach piece called Jesus bleibet Meine Fruede (Joy of Man's Desiring). There are other ways of interpreting a four point perspective. For this particular topic, putting two three-point perspective grids together made sense. (picture to follow soon)
Some quilts are for sale - please contact Elaine at eellisonelaine@yahoo.com for more information and prices.