Mathematician scrutinises Vermeer

The paintings of the Dutch master Johannes Vermeer are a delight to the eye but also provide something special for the mathematician. The design of his paintings appears to have a mathematical basis that dictates the size and placement of the characters he portrayed.

"Using the mathematics within the paintings of Vermeer to construct a camera obscura" is the title of a project at the Esat BT Young Scientist Exhibition prepared by Kate Rowan, a fifth-year student at the Institute of Education. She studied Vermeer's works, analysing them using two formulae familiar to Leaving Cert students.

Vermeer (1632-75) produced striking pictures that have a near photographic quality and accuracy of scale. So rigid was his approach to scale that it became apparent he was likely using some technique to ensure that all objects including people remained within scale.

"It is so close to scale that he must have used some form of device, he wasn't just slapping on the paint," explained Kate. She decided to calculate the scaling and object placement using the formulae to see whether the works followed some mathematical basis.

The indications are that Vermeer did use some method to keep his subjects within scale. Kate suggested a pinhole camera or a lens which could have been used to create a smaller image that in turn could be traced and then used to construct the painting.

Vermeer's The Music Lesson portrays people and objects that are precisely five times smaller than real life, she said. "There seems to be something to do with the number five." His Lady writing a letter with her maid, which hangs in the National Gallery, uses a three times reduction rather than five times.