Doubling the cube (also known as the Delian problem) is one of the three most famous geometric problems unsolvable by compass and straightedge construction. It was known to the Egyptians, Greeks, and Indians.
To "double the cube" means to be given a cube of some side length s and volume V= s3, and to construct the side of a new cube, larger than the first, with volume 2V and therefore side length . The problem is known to be impossible to solve with only compass and straightedge, because ≈ 1.25992105 is not a constructible number.
Famous quotes containing the word doubling:
“My only objection to the arrangements there is the two-in-a-bed system. It is bad.... But let your words and conduct be perfectly pure—such as your mother might know without bringing a blush to your cheek.... If not already mentioned, do not tell your mother of the doubling in bed.”
—Rutherford Birchard Hayes (1822–1893)