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Math and Quilting

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[Symmetry Activity ]


Image:Golden rectangle 1 7ods.jpgMath and Quilting

 Buckey Balls and Bubbles by Elaine Krajenke Ellison

Golden Rectangle 1 by Elaine Krajenke Ellison


Sarah Hinton,  Katelyn Miller, Carrie Churchill


How do quilts use mathematical patterns?  The block is the basic design unit of the quilt top, often squared with many different names used  to describe a guilt design. Log Cabin, Irish Chain and Wedding Ring are among popular block names. As the blocks are repeated  over and over again, a rich pattern of the quilt emerges. Transformation occurs when a shape moves in a plane. Special types of transformations are called isometrics. Three common isometrics in guilts are translation, reflection and rotation. If shapes are slide in the same direction without changing its orientation, so it looks like an exact duplicate of itself, this is translation.  Reflection is flipping a shape over a line, and rotation is turning a shape in a given direction and angle at a fixed point.

Symmetry In Quilting

A quilt box is made of 16 smaller squares, each small consist of 2 triangles. You have H symmetry (capital letter H), when the right half is a mirror image of the left and the top half is a mirror image of the bottom. X and O also have H symmetry. You have M symmetry when the right side is a mirror is a mirror image of the left side, but the top is not a mirror of the bottom.  A and V also have M symmetry.  S symmetry, there are no lines of mirror symmetry, but the figure is the same if you rotate it 180 degrees.  N and Z also have S symmetry.  B symmetry occurs  when the top is a mirror image of the bottom, but the right side is not a mirror of the life side. C and E aslso has B symmetry.

Quilts by Elaine Ellison 

Image:Sacred cut.jpg Sacred Cut

The Sacred Cut comprised of three squares and two Roman Rectangles of proportion square root of two; 1, and two Roman Rectangles of proportion square root of two plus 1:1. Parallel lines must be added at the very center to complete the proportion for the rectangle.  Quilted by Elaine Ellison

Fibonacci X 3

Fibonacci lived from 1175-1250. The number pattern 1,1,2,3,5,8,13,21,34,55,... is attributed to him. The Hindu-Arabic numeration system we still use today, thank to Fibonacci.

Image:Spiraling pythagorean triples--case 1.jpgSpiraling Pythagorean Triples

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

The Six Trigonometrics Functions

The Six Trigonometry goes back to the earlest recorded mathematics in Egypt and Babylon.  In the 2nd century B.C., the astronomer Hipparchus, compiled a trigonometric table for solving triangles. The surrounding tiles are Moorish from the Alcazar.


Making a quilt

Katelyn's Grandmother Quilt