Topology, sometimes called rubber sheet geometry, is an important and young branch of Maths: http://www.gresham.ac.uk/lectures-and-events/surfaces-and-topology
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-events/surfaces-and-topology
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