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M. C. Escher - PowerPoint PPT Presentation

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M. C. Escher. “For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art.”. The Life of Escher. Lived 1898 to 1972 in Holland Was never a good student, even in math Grew to enjoy graphic art and travel

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M. C. Escher

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M. C. Escher

“For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art.”

The Life of Escher

  • Lived 1898 to 1972 in Holland

  • Was never a good student, even in math

  • Grew to enjoy graphic art and travel

  • Became fascinated with geometry and symmetry

The Life of Escher

  • Learned relation to math from brother

    • Crystallography

  • Developed systematic approach for tiling and use of space in planes

  • Became mathematician through his discoveries in art

  • By exploiting many features of geometry, he opened new domain of mathematical art

At first I had no idea at all of the possibility of systematically building up my figures. I did not know ... this was possible for someone untrained in mathematics, and especially as a result of my putting forward my own layman's theory, which forced me to think through the possibilities.

-Escher, 1958

Escher’s Work

  • Began with landscapes

  • Worked through drawings, lithographs, and woodcuts

  • After studying ideas of planes and geometry, developed works with:

    • Tessellations

    • Polyhedron

    • The Shape of Space

    • The Logic of Space

    • Self-Reference


  • Defined as regular divisions of a plane; closed shapes that do not overlap nor leave gaps

  • Previously only known for triangles, squares, and hexagons

  • Escher discovered use of irregular polygons:

    • Reflections, translations, and rotations

    • Use of three, four, or six fold symmetry


  • Platonic solids: polyhedron with same polygonal faces

  • Intersecting or stellating for new forms

  • To make your own polyhedron: Platonic Solid Model

The Shape of Space


Hyperbolic space


The Logic of Space

  • The geometry of space determines its logic, and likewise the logic of space often determines its geometry

    Light and shadow




  • Important concept because of artificial intelligence’s inability to process

Although Escher was not trained as a mathematician, his geometric theoretical discoveries have made a tremendous impact on both the mathematic and artistic worlds.

Student Objectives

  • Learn about:

    • Two-dimensional shapes: sides and angles

    • Geometric concepts: symmetry, congruency

    • Patterns: translations, reflections, rotations

  • Personal expression – visual art

  • Recognize role in real world

Related Materials

  • In order to convey the features of Escher’s mathematical work, many resources may be used:

    • Tangram-tiles

    • Protractors

    • Collect data of polygons and angles for tiling

    • Patterns such as in flooring, quilts, mosaics

    • Creating tessellations: manual, software

Concluding ThoughtsFrom M. C. Escher

Only those who attempt the absurd will achieve the impossible. I think it's in my basement... let me go upstairs and check.

By keenly confronting the enigmas that surround us, and by considering and analysing the observations that I have made, I ended up in the domain of mathematics, Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

The laws of mathematics are not merely human inventions or creations. They simply 'are'; they exist quite independently of the human intellect. The most that any(one) ... can do is to find that they are there and to take cognizance of them.

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