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The Mathematics of Painting

The Mathematics of Painting . Helmer ASLAKSEN Dept. of Mathematics National Univ. of Singapore aslaksen@math.nus.edu.sg www.math.nus.edu.sg/aslaksen/. Giotto, The Flight into Egypt, c1313. Notice how the trees are the same size. Lorenzetti, The Presentation in the Temple, c1342.

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The Mathematics of Painting

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  1. The Mathematics of Painting Helmer ASLAKSEN Dept. of Mathematics National Univ. of Singapore aslaksen@math.nus.edu.sg www.math.nus.edu.sg/aslaksen/

  2. Giotto, The Flight into Egypt, c1313 • Notice how the trees are the same size

  3. Lorenzetti, The Presentation in the Temple, c1342 • Notice how the tiles get smaller

  4. Masaccio, Trinity, 1427 • One of the first perspective pictures

  5. The pavement problem • CD=distance from picture to eye

  6. Where’s the best view point? • 174cm above, 770cm away

  7. Hong Sek Chern,Pigeonholes, 1996 • Use this to find out where to stand

  8. False viewpoints • Pozzo’s ceiling (1694) and cupola (1685) in St. Ignatius, Rome

  9. Anamorphic art • Holbein, The Ambassadors, 1533

  10. Is there perspective in Chinese paintings? • Multiple viewpoints, Chen Chong Swee, Snowscape, 1993 • Raphael, The School of Athens, 1511

  11. Leonardo, The Last Supper, c1497 • The perspective is an integral part of the painting

  12. Changing views on perspective • The different perspectives are an integral part of the painting • Tan Chwee Seng, I Think Hence I Am, 1989 • Montemayor, Barangay Rotunda, 1992

  13. Dürer at the Singapore Art Museum • Dürer, 1527 • Teaching aid or tool for artists?

  14. Perspective at SAM • Ye Shufang, Mathematical Ambiguity, 2002.

  15. What else to see at SAM? • Tessellations

  16. More to see at SAM! • Kaleidoscopes

  17. Even more to do at SAM! • Polyhedra

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