The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.
Duplication of the Cube
a classic problem of geometric construction dating back to ancient times. It is the problem of constructing a cube whose volume is twice that of a given cube. The problem is sometimes called the Delian problem because, according to legend, an oracle said that a plague on Delos, an island in the Aegean Sea, would come to an end if a certain cubic altar were doubled without changing its shape. The problem reduces to the construction of a line segment whose length is equal to 
. As was proved in the 19th century, such a construction cannot be carried out with compasses and straightedge alone. The problem can be solved by making use of, for example, conic sections.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.