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?”

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

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

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.

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

The sixth day of creation 1926 woodcut

Street in Scanno, Abruzzi 1930 woodcut

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

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

Concentric Rinds, 1953 wood cut

Sky and Water II 1938 woodcut

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)

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.

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.

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.”

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

Lets Make A Tessellation

Begin with a simple geometric shape - the square

Change the shape of one side

Copy this line on the opposite side

Rotate the line and repeat it on the remaining edges

Erase the original shape

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

Add color to enhance your picture.

By repeating your shape you create a tessellated picture

.

Escher likedwhat he called“metamorphoses,”

where shapeschanged andinteracted witheach other.

Another example of metamorphosis

Lets make a simple tessellating shape

Begin with a simple geometric shape - the square

Change the shape of one side

Repeat the line on the opposite side

Change the shape of the top

Repeat this line on the bottom

Erase the square

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

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

Add a few line that bring out your hidden shapes.

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

Make four versions of each shape, each version with more detail

The most detailed shape can be changed quite a bit

Make four versions of each shape with more detail

The most detailed shape can be changed quite a bit

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

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

Line up the next most complex with the next simplest

Add the next row in the same way

Completed Tessellation

Completed Tessellation

Completed Tessellation