Type: Seminar

Distribution: World

Expiry: 28 Mar 2014

Auth: seangard@cpe-124-188-249-104.ezsb1.cht.bigpond.net.au (sgar9702) in SMS-WASM

This week’s talk is by Cambridge undergrad Tim Large. Abstract: For such an intuitive geometrical concept, so central to our experience of physical objects, defining curvature has always been somewhat elusive. Trying to pin it down and answer the question "what does it mean for a surface to be curved" is a surprisingly difficult task that requires a fair amount of sideways thought and creativity. This question has dominated geometry over the last 200 years, and a huge variety of ways to approach and answer it have been developed. In this talk, we’ll look at curvature from a select few perspectives. In fact we’ll start over 2000 years ago with Euclid’s axioms of classical geometry, and use them as the point of departure to think about what geometry - the study of lengths, angles, areas - is like on curved surfaces such as on a sphere. We’ll then compare this to the work of Gauss, who applied the machinery of calculus to give the new concept of Gaussian curvature, which bears his name. Finally we’ll briefly discuss how these ideas feed directly into the thoughts Einstein was having around 1915, and produce the backbone of general relativity, a modern physical theory where curvature becomes the mechanism for gravity. Apart from knowing that the sum of the angles of a triangle is 180 degrees (or is it!!), absolutely no prior knowledge of geometry or physics will be needed to follow this talk - just an open mind. Hopefully this talk will be a demonstration of how deep and fascinating simple things can be, and how far ancient ideas can permeate through the most modern of maths and physics.