Math & Art: The Unbeatable Duo

Dear H.S.M. Coxeter,                            June 2, 1959                                                                                  

This is my tile artwork Circle Limit III

I cannot fully express the delight and honor I am experiencing right now, after reading your paper about my sketches. I am so very excited that you see the mathematical perfection within my pieces of art. I am finding myself involving myself more into this realm of mathematics, even though as a child I took no interest in the subject. My brother, Berend sparked my interest in mathematics when he sent me one of Póyla's, the hungarian mathematician, papers from 1924, and now I am thoroughly engrossed in this topic. Even though I have heard that your paper was published four years prior, it has taken due time to reach me. Only fourteen years ago I began to record my thoughts in my notebook and now, wow, I have entered into a whole new phase in my career where I am working with my notes, and translating them into my artwork. In my notebook, that I have decided to name The Regular Division of the Plane with Asymmetric Congruent Polygons, I am attempting to re-create a perspective of infinity on a two dimensional plane. I have also designed a system to categorize shapes so that I can use them in my wood cuttings and sketches. I was so inspired by your paper that depicted how hyperbolic tessellations can be formed using only the diagrams on the paper, and have decided to create my own rules and laws around mathematics in art. The system is quite simple, and I believe it would interest you greatly, so I'll briefly describe it here to you. 
I have split up shapes into two different categories, quadrilaterals, and equilateral triangles, on regular tessellations. From quadrilaterals it branches into variables that define that individual quadrilateral, the type of polygon, and the symmetries in the tessellation. I have assigned a letter to each of the five polygons as seen below.

        A - Parallelogram
B - Rhombus
        C - Rectangle
D - Square
        E - Isosceles Right Triangle

        In my notebook I have created a graph that shows all of the possible symmetries, describing whether the shapes make translations, rotations, glide reflections or a combination of all three. I plan on creating art that represents each shape with the symmetries. Although I have viewed and studied many Moorish sketches, I will make sure that my art doesn't resemble their style, because they refuse to include symbols and shapes from real life. I find it ridiculous, for, how should an artist expect their viewer to relate, if the shapes are not identifiable? I have been, and will continue to work from 8-4 throughout the day until I complete the pieces that include the work from my notebook. I look forward to conversing with you at a future date, and hearing your thoughts on my new findings. In addition, in a few years I strive to have art to show you that represents all of my notes in the book. I neither hope, or wish, to publish my notebook, but will allow you the honor to read it due to our growing friendship. In the future, I hope that our life paths lead to one another.
My best thoughts,
M.C. Escher