1. M.C. Escher and Geometry

2. A little background information…
M.C. Esher was born in the Netherlands in 1898
Dropped out of the School for Architecture and Decorative Arts
Decided to become an artist
Spent much of his life traveling though Italy, which became the inspiration for much of his work
Failed his high school exams

3. Parts, Shapes, and Relationships
Tessellations
Started with basic shapes (triangle, square, hexagon)
Altered them to take the form of animals
Each change had to be compensated
You can see how the triangles in the tessellation on the left were adapted to form the birds on the right. A lot of times he used two different shapes (two different birds) because it is very difficult to create a tessellation with a single image.

4. For Example… When I say each change had to be compensated…
He would start with a square, for instance. (new slide)

5. For Example… Then, he might alter it like this….
So for it to work as a tessellation, he would have to do this. (new slide)

6. For Example…
You can see how those would fit together. Of course, his shapes actually looked like something…

7. 

8. Parts, Shapes, and Relationships
Metamorphosis Images
Start with two-dimensional tessellation
Shift to three dimensions and back
Number of visible planes increases and decreases

9. Parts, Shapes, and Relationships
Strange Loop images
Okay…can anyone tell me what’s wrong with these images?

10. Parts, Shapes, and Relationships
Strange Loop images
Appear to be elevated
Actually on the same plane
Physically impossible structures
Are the structures really physically impossible?

11. Tools and Methods Used basic geometric shapes in his artwork
Repetition
Symmetry

12. Size and Quantity
For a presentation the tessellations would have had to be a manageable size but it really could have gone on infinitely in size.
The metamorphosis images- long and thin, to be read from left to right

13. Why this is important?
Escher’s work shows how art can be enhanced by math, and vice versa
Brings depth to mathematics
Helps us understand geometry