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Number of triangles formed

  1. Mar 28, 2014 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    Find number of triangles which can be obtained by vertices of a regular polygon of n sides.

    3. The attempt at a solution
    I think it should be nC3 as forming a triangle requires you to select any 3 vertices from n available vertices. But I'm not sure whether this is correct or not. Can anyone verify it?
     
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  3. Mar 28, 2014 #2

    Simon Bridge

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    I think the way you would go about verifying something like that would be to draw a bunch of regular polygons, then work out the triangles - count them, and see if it agrees with nC3.
    You'll at least gain confidence with each one that works - but the trick is to see if you can figure out how to get one that won't.
     
  4. Mar 28, 2014 #3

    haruspex

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    You just have to satisfy yourself in regard to four questions:
    1. For any such triangle, is there a selection of three vertices that produces it?
    2. Does every such selection produce a triangle?
    3. Does every such selection produce only one triangle?
    4. For any two such selections, do they produce different triangles?
     
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