Monday, December 01, 2008

Lecture for The Galois Group by Dr. Peter Eccles

Hello hello hello.

Yes - I have finally found time to blog, but first let me advertise the next Galois Group lecture, lest I find myself out of time! Dr. Eccles is no longer Dr. Eccles in my dictionary. He has demanded that I replace Dr. Eccles with Peter! Now as you can imagine I find this quite strange, but Dr. E - well what he doesn't know can't hurt him, and he doesn't know about my blog so I can write Dr. E here if I want to! - seems to be beating me at my own game though. Every time I use Dr. E in an email or person, he replies with a ridiculous formal "substitution" of my name! He doesn't know that Beans has no surname. Pfft. Anyway - it is indeed quite strange to be addressed in such a formal manner, so I have been quite quick in editing my dictionary.

Because of this fiasco I have decided to give every single individual lecturer, who I talk to on a regular basis, the option to substitute "Dr. Z" with their first name! Does that sound better? Pfft again... ANYWAY - times running out so without further ado:

I warmly invite you to attend Dr. Eccles* lecture this Wednesday 3rd December 2008 at 1:10pm in the Alan Turing Building, room G.205 (see abstract/title below). Please do make an even bigger effort to attend, as Dr. Eccles has been a fantastic supporter of The Galois Group from day one and has attended all but one lectures. A fine record indeed! He is a wonderful lecturer and a funny guy too, but if you ask him he'll claim that his "lecture will be boring" (something I learnt when I asked him to "sell his lecture during a topology lecture!). It definitely won't be boring and I will try my best not to embarrass him whilst introducing him.... MUHAHAHAHA :D

See you on Wednesday.

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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.

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Free refreshments are available at the end and for further information or any queries please feel free to contact Dr. M.D Coleman or myself.

* I don't know where the bloody apostrophe is meant to go - humbug!

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