doubling the cube

geometry

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June 25, 2026

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The "doubling the cube" problem, also known as the Delian problem, is a classic geometry challenge. It asks for the construction of a cube with double the volume of a given cube. This means finding the edge length, x, such that x³ = 2a³, where a is the edge of the original cube.12

The problem is equivalent to finding two mean proportionals between a line segment and its double. Ancient Greek mathematicians, like Hippocrates, showed that this problem could not be solved using only a straightedge and compasses. While it remained impossible with these tools, the Greeks were able to find solutions using more complex curves. The problem's name originates from an ancient Greek oracle's decree that a plague in Athens could be ended by doubling the size of a cubical altar to Apollo.13

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conic section
Greek origins
…joined to the problem of “doubling the cube.” According to Eratosthenes of Cyrene (c. 276–190 bc), the people of Delos consulted the oracle of Apollo for aid in ending a plague (c. 430 bc) and were instructed to build Apollo a new altar of twice the old altar’s volume and…
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…joined to the problem of “doubling the cube.” According to Eratosthenes of Cyrene (c. 276–190 bc), the people of Delos consulted the oracle of Apollo for aid in ending a plague (c. 430 bc) and were instructed to build Apollo a new altar of twice the old altar’s volume and…
Read More

mathematics
The three classical problems
…known as the “classical problems”: doubling the cube (i.e., constructing a cube whose volume is twice that of a given cube), trisecting the angle, and squaring the circle. Even in the pre-Euclidean period the effort to construct a square equal in area to a given circle had begun. Some related…
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…known as the “classical problems”: doubling the cube (i.e., constructing a cube whose volume is twice that of a given cube), trisecting the angle, and squaring the circle. Even in the pre-Euclidean period the effort to construct a square equal in area to a given circle had begun. Some related…
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Hippocrates of Chios
…of the problem of “doubling the cube” (a three-dimensional quantity) to finding two lengths (one-dimensional quantities) certainly fits this description.
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…of the problem of “doubling the cube” (a three-dimensional quantity) to finding two lengths (one-dimensional quantities) certainly fits this description.
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