## Duplicating the Cube

Duplicating the Cube:

The problem of duplicating the cube is nowhere near as well known as the other two — trisecting the angle and squaring the circle. The traditional story is that an altar in the shape of a perfect cube must be doubled in volume. This is equivalent to constructing a length of $\sqrt{2}$ starting from the rational points of the plane. The desired length satisfies another cubic equation, this time the obvious one, $x^{3}-2=0$. For the same reason that trisecting the angle is impossible, so is duplicating the cube, as Pierre Wantzel pointed out in his 1837. Cube -duplications are so rare you hardly-ever come across one. Trisectors are ten a penny.

More later,

Nalin Pithwa