M.C. Escher was a Dutch graphic artist

Tessellations By: Victoria Miles Math 2204 Group 2 • For this independent study, my project is on Escher’s Art and his work with tessellations. Throughout my presentation, I will discuss and display pieces of Escher’s work and give a brief description of his life. I will also focus on how math and art are put together to create tessellations and on the main points of how his art is formed. • Full name is Maurtis Cornelis Escher • Born June 1898, and died in March of 1972 • Escher was born in Leeuwardens, in the Netherlands • Escher was the 4th and youngest son of an engineer. • This is an example of Eschers lithography, called Belvedere. (1958) • After Escher failed his high school exams he studied at the School of Architecture and Ornamental Design in Harlem from 19191922. • M.C. Escher was a Dutch graphic artist, most recognized for spatial illusions, impossible buildings, repeating geometric patterns(tesselations) and his incredible techniques in woodcutting and lithography. • Escher is best known for his work with tesselations. • He has lived and worked in Italy, the Netherlands, Belgium & Switzerland. • In Italy he met his future wife Jetta Umiker, they married in 1924. • Escher considered himself neither and artist or a mathematician. • What is a tessellation? A tessellation is basically a repeating pattern of interlocking shapes. • In each of the interlocking shapes, half the boundary,or line, is a clone of the other half. • These identical boundaries assure that the interlocking shapes will mend together, without any gaps. • Tessellate means to form or arrange small squares in a checker board mosaic pattern • it is derived from the Ionic Greek word “tesseres”, which in English means 4. • Mathematics is brought into this art mainly through symmetry and geometry. • Translation, Rotation and Reflection are used when creating tessellations. • Tessellations are 1000’s of years old, and can be traced back as far as the 4000 BC, in the Summerian Civilization. • They were used at the time to decorate houses and temples. And were made of slabs and clay instead of fabrics. • Patterns for quilts • study of math (geometry) • patterns for tire treads • patterns for shoe bottoms • stained glass windows • needle point • Parking lot design • cubical layout • interlocking ceramic tile design • X-ray image of DNA crystal shows the double helix structure • art ; Easter egg design How Do You Know if a Shape Will Tessellate??? • In order for a shape to be used in a tessellation the shape must have an interior angles which divide 360 evenly. • Example: THE HEXAGON • hexagon has interior angles of 120 degrees ; 360/120 = 3 (evenly divided number, it WILL tessellate) • This is a part of an essay written by Escher on tessellations. • “In mathematical quarters,the regular division of the plane has been considered theoretically…Does this mean that it is an exclusively mathematical question? In my opinion, it does not. (Mathematicians) have opened the gate to leading to an extensive domain, but they have not entered this domain themselves. By their very nature thay are more interested in the way in which the gate is opened than in the garden lying behind it” • This is made of interlocking parallelograms • to fit together, the shape has to be translated, or shifted diagonally. • Math is brought into this art through congruency. • 1) Take a square and cut out a shape in one of the sides. • 2) Tape the shape to the opposite side of the square. • 3) Cut the entire new shape in half again in any pattern you want. • 4) Then tape the 2 opposite halves together (straight edges taped) • 5) Continue this and stick all the shapes together for a tessellation. “So let us then try to climb the mountain, not by stepping on what is below us, but to pull us up at what is above us, for my part at the stars; amen.” -M.C. Escher • • • • • http://www.worldofescher.com http://www.mathforum.com http://www.tessellations.com http://www.mcescher.com Compton's Interactive Encyclopedia 1997 Edition • Book ( Contemporary Math Pg 313-315 ) • Folder on Escher in the Library