M.C Escher's drawings were of mind boggling structures that logically would be impossible in three dimensional space. Some of these drawings were based on the work of British mathematician
Sir Roger Penrose. In 3-dimensional analytic geometry the shape of an object is not only determined by the positions of the vectoral lines, but also by the position of the observer. It is understanding of this math that lead to the development of these models.
Mathematicians have theoretically mapped out the regular divisions of a plane because this is part of crystallography. Does it therefore belong exclusively to mathematics? I do not think so. Crystallographers have given us a definition of the concept and have researched and determined what and how many systems and methods exist for dividing a plane regularly. By doing this they have opened the gate that gives access to a vast domain, but they themselves have not entered. Their nature is such that they are more interested in the way the gate is opened than in the garden that lies behind it.(M.C.ESCHER)
