The Mathematics of Painting

Helmer ASLAKSENDept. of Mathematics

National Univ. of Singaporeaslaksen@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

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