The Mathematics of Painting
Helmer ASLAKSENDept. of Mathematics
National Univ. of [email protected]
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
Notice how the tiles get smaller
Masaccio, Trinity, 1427
One of the first perspective pictures
The pavement problem
CD=distance from picture to eye
Where’s the best view point?
174cm above, 770cm away
Hong Sek Chern, Pigeonholes, 1996
Use this to find out where to stand
False viewpoints
Pozzo’s ceiling (1694) and cupola (1685) in St. Ignatius, Rome
Anamorphic art
Holbein, The Ambassadors, 1533
Is there perspective in Chinese paintings?
Multiple viewpoints, Chen Chong Swee, Snowscape, 1993 Raphael, The School of Athens, 1511
Leonardo, The Last Supper, c1497
The perspective is an integral part of the painting
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
Dürer at the Singapore Art Museum
Dürer, 1527 Teaching aid or tool for artists?
Perspective at SAM
Ye Shufang, Mathematical Ambiguity, 2002.
What else to see at SAM?
Tessellations
More to see at SAM!
Kaleidoscopes
Even more to do at SAM!
Polyhedra