median
don steward
mathematics teaching 10 ~ 16

Sunday, 5 May 2013

pyramids and prisms and Euler

these are representations of the pyramid family:

what do they all have in common?

how would you describe a pyramid to someone who wasn't clear?








can you explain why there are the same number of faces as there are vertices?

what is the relationship between the number of arcs and the number of vertices?
why?

Euler's relationship is F + V = E + 2
faces + vertices = edges + 2

why must this be true for any pyramid?

these are representations of the prism family:

what is the common feature of this family of solids?

can you explain why for each prism, the numbers of vertices and the numbers of edges are in the same multiplication table?




what is the relationship between the number of faces and the number of vertices?
why?

why must Euler's relationship be true for any prism?

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