Sariaht
Jan16-04, 04:04 PM
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.
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.