Surfaces and Topology - Professor Raymond Flood

Topology, sometimes called rubber sheet geometry, is an important and young branch of Maths: http://www.gresham.ac.uk/lectures-and... If we count the number of vertices, v, on a cube, v = 8, number of edges e = 12, and number of faces f = 6, then v¬ -- e + f = 2. The same is true for a tetrahedron where v¬ = 4, e = 6 and f = 4. In fact, the mathematician Leonhard Euler obtained the amazing result that v¬ -- e + f = 2 for a wide class of polyhedrons. This theorem of Euler is a result in topology, a subject which tries to find those properties of geometrical objects that are invariant under continuous deformation -- a tetrahedron can be changed in this way into a cube. The transcript and downloadable versions of the lecture are available from the Gresham College website: http://www.gresham.ac.uk/lectures-and... Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently over 1,500 lectures free to access or download from the website. Website: http://www.gresham.ac.uk Twitter:   / greshamcollege   Facebook:   / greshamcollege