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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}= a^{2}+ b^{2}+ 2ab

a b

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Inside the square, there is another square, c^{2}.

it cuts between a and b on all 4 sides. What's left is 2ab

so a^{2}+ b^{2}= c^{2}

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

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# Fermat’s Theorem

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