Fermat’s Theorem

Sariaht

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.