M.C. Escher

1. M.C. Escher “I believe that producing pictures, as I do, is almost solely a question of wanting so very much to do it well?”

2. Early Life • Maurits Cornelis Escher 1898-1972 • Born in the Netherlands • Youngest of 5 • Father was a civil engineer

3. Education • Attended both elementary and secondary school but did not do very well. His interest was in music and carpentry. • Math was very difficult for him. “At high school in Arnhem, I was extremely poor at arithmetic and algebra because I had, and still have, great difficulty with the abstractions of numbers and letters. When, later, in stereometry (solid geometry), an appeal was made to my imagination, it went a bit better, but in school I never excelled in that subject. But out path through life can take strange turns.” M.C.Escher

4. Developed interest in printing techniques • Failed his final exams and so he never officially graduated • Attended Higher Technical School in Delft • 1920 he moved to Haarlem and study architecture, an attempt to follow his father’s wishes, at the school for Architecture and Decorative arts.

5. Met Samuel Jesserum de Mesquita, graphic arts teacher. • Escher was convinced that the graphic design program would better suit his skills. (wood cuts) • After school traveling took up a large part of Escher’s life from this point on. • Traveled Italy extensively sketching and drawing. Atrani, Coast of Amalfi 1931Lithograph

6. The sixth day of creation 1926 woodcut Street in Scanno, Abruzzi 1930 woodcut

7. Family • Met his wife Jetta Umiker in 1923 • 3 kids, George, Arthur and Jan • Took his family all over Italy • Letter to his son Reptiles 1943 Lithograph

8. Mathematics • October 1937 Escher showed some of his new work to his brother Berend, a professor of geology at Leiden University. • Recognized a connection between Escher’s wood cuts and crystallography. • Berend sent his brother a list of articles for him to read. • This was Escher’s first contact with mathematics. Smaller and Smaller 1956, wood engraving and wood cut in black and brown printed from 4 blocks

9. Concentric Rinds, 1953 wood cut Sky and Water II 1938 woodcut

10. Family life • Escher made numerous woodcuts utilizing each of the 17 symmetry groups • His art formed an important part of family life. • Escher worked in his study 8am- 4pm every day. • New concepts could take months or even yrs to develop before the work was discussed and explained to the family. (son’s letter)

11. Work • Around 1956 Escher’s interests changed again taking regular division of the plane to the next level by representing infinity o a fixed 2-dimensional plane. Earlier in his career he had used the concept of a closed loop to try to express infinity as demonstrated in Horseman, 1946.

12. Tessellations • Escher was introduced to hyperbolic tessellations • This style of artwork required enormous dedication because of the careful planning and trial sketches required, coupled with the necessary hand ad carving skill.

13. Achievement • 1995 Coxeter published a paper which proved that Escher had achieved mathematical perfection in one of his etchings. Circle Limit III, 1956 was created using only simple drawing instruments and Escher’s great intuition, but Coxeter proved that “… [Escher] got it absolutely right to the millimeter, absolutely to the millimeter… Unfortunately he didn’t live long enough to see my mathematical vindication.”

14. By 1958 Escher had achieved remarkable fame. • Gave lectures and corresponded wit people who were eager to learn from him • Gave his first important exhibition of his works and was featured on Time magazine. • Received numerous awards over his career. Printed from 33 blocks on 6 combined sheets

15. Lets Make A Tessellation

16. Begin with a simple geometric shape - the square

17. Change the shape of one side

18. Copy this line on the opposite side

19. Rotate the line and repeat it on the remaining edges

20. Erase the original shape

21. Add lines to the inside of the shapes to turn them into pictures.

22. Add color to enhance your picture.

23. By repeating your shape you create a tessellated picture

24. Escher likedwhat he called“metamorphoses,” . where shapeschanged andinteracted witheach other.

25. Another example of metamorphosis

26. Lets make Lets make a simple tessellating shape a metamorpasis Tessellation

27. Begin with a simple geometric shape - the square

28. Change the shape of one side

29. Repeat the line on the opposite side

30. Change the shape of the top

31. Repeat this line on the bottom

32. Erase the square

33. Turn shape looking for two hidden animals, flowers, fish, insects, or birds.

34. Draw a line that separates the two hidden shapes you have found.

35. Add a few line that bring out your hidden shapes.

36. Separate the two shapes so you can use them one at a time

37. Make four versions of each shape, each version with more detail The most detailed shape can be changed quite a bit

38. Make four versions of each shape with more detail The most detailed shape can be changed quite a bit

39. Color all of one type of shape the same basic color scheme

40. Line up the simplest shape with the most complex along the bottom

41. Line up the next most complex with the next simplest

42. Add the next row in the same way

43. Completed Tessellation

44. Completed Tessellation

45. Completed Tessellation