Friday, 21 November 2008

Dr. Peter Eccles lectures for The Galois Group - Wednesday 3rd December 08

Dear All,

You are invited to attend the next Galois Group lecture, which will be given by Dr. Peter Eccles on Wednesday 3rd December 2008 at 1:10-2pm in the Alan Turing Building (room G.205). Please see the abstract below and do recall that registration is not required - you just have to turn up! Free refreshments are also available at the end.

For further information or any queries please feel free to contact Dr. M.D Coleman or myself.

Best wishes,

Wednesday 3rd December 2008 at 1:10-2pm
Alan Turing Building, room G.205

Peter Eccles

Abstract - From Perspective to the Projective Plane

During the fifteenth century artists made significant advances in the use of perspective in order to give an impression of depth in their pictures. Leon Battista Alberti wrote the first text on this subject in 1435. I will describe his method for drawing a square tiled pavement and illustrate it using a photograph of the Alan Turing Building taken by Nick Higham.

Alberti's work led to questions about what geometrical features different views of the same object might have in common. The answer to this question was provided by Girard Desargues in 1639 with the introduction of projective geometry. In this, additional 'points at infinity' are added to the Euclidean plane so that any pair of straight lines in the plane meet at a unique point (which is a point at infinity if the lines are parallel). This feature is observed when viewing straight railway lines going into the distance: they appear to meet at a point at infinity. I will give an example of how Desargues was able to unify certain disparate results in Euclidean geometry, by observing that they are all special cases of a single result in projective geometry.

In more modern times, topologists have studied the projective plane as a single object in its own right. In 1902, Werner Boy constructed a model of the projective plane in three dimensional Euclidean space. I will describe one method for constructing this model. I will also mention some unsolved problems relating to models of this type.