5th December 2012 at 8pm
"How Round is Your Circle?" by Dr Chris Sangwin
Mechanisms are all around us. We often take them for granted, or don't even notice they exist. Most have a long and interesting history.
Almost all such mechanisms rely on rotating parts. That is, one circular part which fits inside another. These need to be made very accurately to work safely, smoothly and without wearing out.
This raises a basic problem which links engineering to mathematics. How do you test if something is round? I.e., how round is your "circle"? Sounds simple? The answer to this question turns out to be much more interesting than it first appears. It involves the shape of the 50p coin, the NASA Space Shuttle Challenger explosion in 1986 and how to drill a square hole.
16th January 2013 at 8pm
"How Big is Infinity?" by Dr Chris Good
Just how big is infinity? Bigger than you might think. It turns out that there are infinitely many infinities and that given any infinity there is a bigger one.
In this talk we will prove that there are at least two infinities and along the way touch on ideas of Georg Cantor that split the mathematical community at the end of the 19th century.
6th February 2013 at 8pm
"Mathematics Under the Lens" by Dr Richard Kaye
The first lens that successfully records straight lines in the subject as straight lines in the image was introduced simultaneously by Dallmeyer and Steinheil in 1866. Known as the "rapid rectilinear" or "aplanat" lens, it was a significant improvement on previous lenses.
We will explore the geometry of transformations that preserve straight lines, and give a number of illustrations and creative techniques in photography that illustrate the use of rectilinear lenses. This talk will look at some of the geometry behind camera lenses.
13th March 2013 at 8pm
"The Maths of Google" by Dr Richard Lissaman
Internet search engines and video graphics are both multi-billion pound global industries. And maths is at the heart of both of them. Google depends on simultaneous equations, while the graphics behind computer animated films and games require thousands of calculations involving triangles, angles and vectors. In this session we’ll look at applications of school level mathematics in internet search engines and video games.
Richard Lissaman is Programme Leader of the Further Mathematics Support Programme. He has been a lecturer at Warwick University, and for a couple of years he also worked part time advising a computer games company in London. Richard has a PhD in algebra and is an author of maths textbooks.
17th April 2013 at 8pm
"Could a Baby Robot Grow Up to Be a Mathematician?" by Professor Aaron Sloman
Euclidean geometry is one of the greatest products of human minds, brought together in Euclid's Elements over two millenia ago.
However, at some distant earlier time there were no geometry textbooks and no teachers. So, long before Euclid, our ancestors, perhaps while building huts, temples and pyramids, or making tools or weapons, or measuring fields, or reasoning about routes, must have noticed facts about spatial structures and processes that are not only useful, but, unlike facts of physics, chemistry and biology, are provable by reasoning, without having to keep checking that they remain true at high altitudes, or in cold weather, or on surfaces with unusual materials or colours.
Without teachers to help, biological evolution must somehow have produced information-processing mechanisms that allowed ancient humans to develop the concepts, notice the relationships and discover the proofs that later humans normally encounter at school, but which we have the ability to discover for ourselves, as our ancestors did.
All this suggests that normal human children have the potential to make those discoveries, under appropriate conditions. I suspect there are deep connections with competences that have evolved in other intelligent species that understand spatial structures, relationships and processes -- such as nest-building birds, squirrels working out how to get nuts from bird feeders, elephants that manipulate water, mud, sand and foliage with their trunks, and apes coping with many complex structures as they move through and feed in tree-tops.
One way to demonstrate the feasibility of this conjecture is to try to design a robot that starts off with the competences of a very young child and develops in similar ways, extending those competences, and later perhaps being stimulated by the environment to make simple discoveries in Euclidean geometry -- unlike current geometric reasoning programs that use cartesian coordinate representatons of geometrical structures.
How to do this is not at all obvious. There have been great advances getting computers to reason logically, algebraically and arithmetically, but the kinds of reasoning in Euclid, e.g. using diagrams, are very different. I'll discuss some of the problems and possible ways forward. Perhaps someone now studying geometry at school will one day design the first baby robot that grows up to be a self-taught robot geometer, and, like some of our ancestors, discovers for itself why the angles of a planar triangle must add up to exactly half a rotation?