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