The regular division of the plane involves covering the plane with the same piece, repeated regularly without leaving any gaps.

1.- One of the most outstanding features of Escher's paintings and engravings was the use of regular division of the plane.

2.- Escher was fascinated by the mosaics and tessellations which decorated Muslim architecture. However, in his works he transforms these abstract geometric motifs into concrete ones which are easily recognized.

3.- In order to design his own constructions he studied the rules governing regularity and compiled a notebook of his findings between 1941 and 1942. The drawing illustrated in this window is commonly called "birds".

"I find it hard to believe that something as obvious as drawing shapes which complement each other has never occurred to anyone else" (Escher).

However, if we look closely at Escher's engravings we can see that the degree of complexity in some cases is outstanding. The goal is to find one particular shape which, after a series of geometric movements, can be used to cover the plane completely.

4.- By this point you should have sufficient knowledge of maths to be able to identify the different geometric movements which are illustrated in the window.

5.- We start with a fish. This same fish is repeated across the plane until it is completely covered. Try to identify the geometric movements needed in order to cover the plane, starting with one set fish.

6.- The mosaic in this window is Regular Division of the Plane nº 99, VIII, 1954.

7.- Do you think it is easy to design a piece which, when joined together with other identical pieces, would cover the surface of a table like a jigsaw puzzle, without leaving any gaps? This unit will show you how important the mathematical aspect of doing this is.

Escher soon mastered the gradual and continuous change technique that a regular polygon undergoes until different animal shapes emerge. One of his most famous works is the mural Metamorphosis. The work itself provides the strategies needed to create pieces and the necessary relevant changes.

8.- One example which is characteristic of this field is illustrated in this window, which shows part of the lithograph Reptiles (1943).

9.- In this engraving the reptile does not just remain on the plane. It is translated from the two-dimensional space of the plane into three-dimensional space in such a way that it is drawn out of the paper, moved slightly and then put back again to form part of the tessellation of the plane. Choose different images in this engraving and look carefully at what happens to them.

10.- Escher wasn't just a master of tessellating the plane. His mathematical curiosity lead him to investigate modern geometry, which differed from traditional Euclidean geometry, such as hyperbolic geometry and other concepts like the concept of infinity.

11.- Other series of well-known works include those illustrating impossible objects or situations, which at times even challenge the laws of physics.