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M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in...

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M.C. M.C. Escher Escher Jamie Jamie Gilbertson Gilbertson Math 471 Math 471 Fall 2005 Fall 2005
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Page 1: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

M.C. EscherM.C. EscherJamie GilbertsonJamie Gilbertson

Math 471Math 471Fall 2005Fall 2005

Page 2: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

Full name: Maurits Cornelis EscherFull name: Maurits Cornelis Escher

Born in Leeuwarden, Holland on Born in Leeuwarden, Holland on

June 17,1898June 17,1898

Entered secondary school in 1912 where Entered secondary school in 1912 where he did not enjoy mathematics, but he liked he did not enjoy mathematics, but he liked art class.art class.

BackgroundBackground

Page 3: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

““I was extremely poor at arithmetic I was extremely poor at arithmetic and algebra because I had, and still and algebra because I had, and still have, great difficulty with the have, great difficulty with the abstractions of numbers and letters. abstractions of numbers and letters. When, later, in stereometry [solid When, later, in stereometry [solid geometry], an appeal was made to geometry], an appeal was made to my imagination . . . but in school I my imagination . . . but in school I never excelled in that subject” never excelled in that subject”

-M.C. Escher-M.C. Escher

Page 4: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

His Start in ArtHis Start in ArtTraveled to Italy and began Traveled to Italy and began drawing sketches of the trees and drawing sketches of the trees and vistas. vistas.

Fascinated with structure and Fascinated with structure and lightlight

Paid careful attention to details of Paid careful attention to details of the roof shingles and the the roof shingles and the cobblestone path wayscobblestone path ways

Page 5: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

His attraction to plane geometry began to His attraction to plane geometry began to grow.grow.

Visited the Alhambra and became very Visited the Alhambra and became very influenced by the Moor Civilizationinfluenced by the Moor Civilization

Constructed tessellations using Constructed tessellations using interlocking polygons.interlocking polygons.

Geometry and TessellationsGeometry and Tessellations

Page 6: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

Though the Moor Civilization was Though the Moor Civilization was forbidden from using living forbidden from using living creatures in their art, Escher took a creatures in their art, Escher took a great interest in using these figures great interest in using these figures

Used mainly birds, lions, and fishUsed mainly birds, lions, and fish

Page 7: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

Uses of SymmetryUses of Symmetry

TranslationTranslation

RotationRotation

ReflectionReflection

Glide-ReflectionGlide-Reflection

Page 8: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

TranslationTranslation RotationRotation

Translation & RotationTranslation & Rotation

Page 9: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

ReflectionReflection Glide-ReflectionGlide-Reflection

Reflection & Glide-ReflectionReflection & Glide-Reflection

Page 10: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

Putting it all TogetherPutting it all Together

Page 11: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

Used a fading technique to blend objects Used a fading technique to blend objects together.together.

Constructed the famous Metamorphose Constructed the famous Metamorphose series.series.

Metamorphose I

Page 12: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

Became Became fascinated with fascinated with the concept of the concept of infinity and began infinity and began reflecting this into reflecting this into his art.his art.

InfinityInfinity

Page 13: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

The Possible ImpossibilitiesThe Possible Impossibilities

Began constructing art that defied that Began constructing art that defied that natural laws of human naturenatural laws of human nature

3

Page 14: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

The WaterfallThe Waterfall

Page 15: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

BelvedereBelvedere

Page 16: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

RelativityRelativity

Page 17: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

““What pathetic slaves we turn out to What pathetic slaves we turn out to be of gravity’s dominant power over be of gravity’s dominant power over everything on earth. And then the everything on earth. And then the right angle between the horizontal right angle between the horizontal and the vertical! Almost everything and the vertical! Almost everything we construct … are all right-angled we construct … are all right-angled boxes. They really are dreadfully boxes. They really are dreadfully boring and annoying.”boring and annoying.”

-M.C. Escher -M.C. Escher

Page 18: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

The Possible ImpossibilitiesThe Possible Impossibilities

With his fascination of infinity, he With his fascination of infinity, he created two never ending created two never ending illustrations:illustrations:– Drawing HandsDrawing Hands– MMööbius Stripbius Strip

Page 19: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

Drawing HandsDrawing Hands

Page 20: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

MMööbius Strip IIbius Strip II

Page 21: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

"An endless ring-shaped band usually "An endless ring-shaped band usually has two distinct surfaces, one inside has two distinct surfaces, one inside and one outside. Yet on this strip nine and one outside. Yet on this strip nine red ants crawl after each other and red ants crawl after each other and travel the front side as well as the travel the front side as well as the reverse side. Therefore the strip has reverse side. Therefore the strip has only one surface." only one surface."

-M.C. Escher -M.C. Escher

Page 22: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

In the EndIn the End

In the late 1960s, his health became very In the late 1960s, his health became very poor.poor.

Continued to complete his mathematical Continued to complete his mathematical creations into his later days.creations into his later days.

Died in March of 1972Died in March of 1972

Page 23: M.C. Escher Jamie Gilbertson Math 471 Fall 2005. Full name: Maurits Cornelis Escher Born in Leeuwarden, Holland on June 17,1898 Entered secondary school.

Works CitedWorks Cited

Visions of SymmetryVisions of Symmetry by Doris by Doris Schattschneider Schattschneider © 1990© 1990

The Official M.C. Escher WebsiteThe Official M.C. Escher Website

www.mcescher.comwww.mcescher.com

The Geometry CenterThe Geometry Center


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