Post by Kimberly Adams on May 18, 2007 16:28:05 GMT -5
A tesselation is regular divisions of a plane. Tesselations are when shapes and figures take up the entire plane, leaving no gaps and having no overlaps. Most tesselations are with normal polygons, such as bath tiles.
Escher was fascinated, though, with a different, more complex tesselation, called (by himself) a "Metamorphoses"-where shapes changed and could seem to come to life, exiting/entering the plane or interacting with each other or other things. A great example would be "Reptiles".
[[ note to self: Put url here for reptiles. ]]
An excerpt from a report (off Mathmatical Art of... website-see citations) by Escher after seeing "Metamorphoses" in Spain:
"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 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. "
Well, of course he sounds rude, but slightly humorous in the sense of his last line. Yet, Escher does have a point, mathematician's have concluded that of all regular polygons, only the triangle, square, and hexagon can be used in a tesselation. Escher did follow the rules though, however changing them slightly. He did what geometry teaches, about transformations-reflections, traslations, and rotation. Escher only changed the regular polygon's to make them resemble an animal or thing.
Escher was fascinated, though, with a different, more complex tesselation, called (by himself) a "Metamorphoses"-where shapes changed and could seem to come to life, exiting/entering the plane or interacting with each other or other things. A great example would be "Reptiles".
[[ note to self: Put url here for reptiles. ]]
An excerpt from a report (off Mathmatical Art of... website-see citations) by Escher after seeing "Metamorphoses" in Spain:
"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 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. "
Well, of course he sounds rude, but slightly humorous in the sense of his last line. Yet, Escher does have a point, mathematician's have concluded that of all regular polygons, only the triangle, square, and hexagon can be used in a tesselation. Escher did follow the rules though, however changing them slightly. He did what geometry teaches, about transformations-reflections, traslations, and rotation. Escher only changed the regular polygon's to make them resemble an animal or thing.