The Euler Number (Geometry and the Imagination)
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Conway, Doyle, Gilman, Thurston; The Geometry Center  
If we have a polyhedron, we can compute its Euler number, x=VE+F. In fact, we computed Euler numbers ad delectam. Why did we do this? One reason is that they are is easy to compute. But that is not obviously a compelling reason for doing anything in mathematics. The real reason is that it is an invariant of the surface (it does not depend upon what map one puts on the surface) and because it is connected to a whole array of other properties a surface might have that one might notice while trying to describe it. One easy example of this is Descartes' formula...  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Lesson Plans and Activities 
Math Topics:  e, Differential Geometry 
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