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Fermat’s Theorem

  1. Jan 16, 2004 #1
    Any interesting thoughts?

    a cube have 6 sides and 8 corners, you cannot make one cube fit into another.

    But a square has 4 sides and 4 corners, therefore you can make one fit into another.

    An n-dimensional object has got lesser corners than sides, therefore you can make no n-dimensional object fit into another perfectly, when n>2.

    (a + b)2 = a2 + b2 + 2ab


    a b
    ------|-----

    Inside the square, there is another square, c2.
    it cuts between a and b on all 4 sides. What's left is 2ab

    so a2 + b2 = c2

    An n-dimensional object inside another cannot cut all sides into whole numbers since it cannot cut all sides at all for n>2.
     
  2. jcsd
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