Answer to Question #336821 in Geometry for Mazet

Question

What is doubling the cube means?

Answer 1

doubling the cube means constructing a cube whose volume is twice that of a given cube. The problem requires the construction of the edge of a second cube whose volume is double that of the first.

Doubling a unit cube requires the construction of a line segment of length x, where x³ = 2; in other words, x = 2^1/3 , the cube root of two. This is because a cube of side length 1 has a volume of 1³ = 1, and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2. The impossibility of doubling the cube is therefore equivalent to the statement that  is not a constructible number.

Doubling the cube is now known to be impossible to construct by using only a compass and straightedge