Transcript The Mathematics of Painting

The Mathematics of Painting
Helmer ASLAKSEN
Dept. of Mathematics
National Univ. of Singapore
[email protected]
www.math.nus.edu.sg/aslaksen/
Giotto, The Flight into Egypt,
c1313
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Notice how the trees are the same size
Lorenzetti, The Presentation in
the Temple, c1342
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Notice how the tiles
get smaller
Masaccio, Trinity, 1427
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One of the first perspective pictures
The pavement problem
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CD=distance from picture to eye
Where’s the best view point?
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174cm above, 770cm away
Hong Sek Chern, Pigeonholes,
1996
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Use this to find out where to stand
False viewpoints
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Pozzo’s ceiling (1694) and cupola (1685) in
St. Ignatius, Rome
Anamorphic art
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Holbein, The Ambassadors, 1533
Is there perspective in Chinese
paintings?
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Multiple viewpoints, Chen Chong Swee,
Snowscape, 1993
Raphael, The School of Athens, 1511
Leonardo, The Last Supper,
c1497
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The perspective is an integral part of the
painting
Changing views on perspective
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The different perspectives are an integral part
of the painting
Tan Chwee Seng, I Think Hence I Am, 1989
Montemayor, Barangay Rotunda, 1992
Dürer at the Singapore Art
Museum
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Dürer, 1527
Teaching aid or tool for artists?
Perspective at SAM
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Ye Shufang, Mathematical Ambiguity, 2002.
What else to see at SAM?
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Tessellations
More to see at SAM!
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Kaleidoscopes
Even more to do at SAM!
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Polyhedra