Mathematical Quilts

Some of my work...
       

 Delightfully Dutch Dissection - In this Dutch Chintz quilt, the heart and the ellipse
are the focus of the one-point perspective. The heart and ellipse are part of a
twisted hinge dissection. A dissection is made from cutting a figure and repositioning it.
If the heart is cut in half so each part of the heart matches up with the other, one
of the parts can be rotated through l80 degrees in space. The resulting figure is
the ellipse! Likewise, half of the ellipse can be rotated to form the heart!
Purdue Professor Greg Frederickson inspired this fascinating quilt.

 


   

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.


 

Bach's Jesus bleibet meine Freude - A four-point perspective: Elizabeth Ahlgrim, a harpist in the Indianapolis area, posed for this quilt. Playing the Bach piece on her pedal harp was quite a delight to hear. The curvature of the harp and harpist is due to the four-point perpsective grid. This four-point perspective places two three-point perspective grids together.




    

Fablous Fibonacci Flowers - A five-point perspective.

  

          

 

Perspective of Paradise -  This 6 point perspective was inspired by Dick Termes
and his work on perspective systems.  The 6 point perspective originates from
utilizing two 5 point perspectives, each of l80 degrees, and placing them back to back.
The newly created artwork is a 360 degree view of paradise.  The 6 vanishing points
on the flat surface are found by using north, east, south, and west positions.
The 5th and 6th vanishing points are achieved by adding a point at the
center front position and center back position.



   

    Atmospheric Perspective Golden Rectangle at Giverny - It is difficult to pinpoint
the time of origin of the golden rectangle,  but most certainly the Golden Rectangledates
back to at least 1,000 B.C. Descartes  studied the golden rectangle thoroughly in 1638.
Jaques Bernoulli was fascinated by  its’ properties also. His statement “eadem mutata resurgo” refers to the fact that the  angle formed from the tangent to the curve remains at a constant angle throughout.  The spiral inscribed in the Golden Rectangle 1 quilt is an approximate logarithmic spiral. This is a great example of an atmospheric perspective.





Greco Roman Perspective Mathematical Harmony - Music, like mathematics, has an
abstract notation that is used to represent abstract structures. Like mathematics,
the notation has developed over the centuries. "Military Polonaise" by Chopin can be found
in the background of this quilt. The four major instrument groups are represented
by the violin, the b-flat clarinet, the piano, and the double french horn. The Greek mathematician Pythagoras (c. 569 B.C.E. - c. 507 B.C.E.) is credited with discovering
the harmonic progression in the notes of the music scale by finding the musical
intervals and the pitch of the notes corresponding to the relative length of vibrating strings. He discovered that if a string was plucked in a 1:2 ratio, an octave is obtained. Similarly,
a fifth is obtained from a 2:3 ratio, and a fourth by a 3:4 ratio. 
       

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