# Doubling the Cube by Compass and Straightedge Construction is Impossible

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## Contents

## Theorem

There is no compass and straightedge construction to allow a cube to be constructed whose volume is double that of a given cube.

## Proof

## Also known as

The problem of **Doubling the Cube** is known as **the Delian problem**, after the location (Delos) of the altar whose dimensions were under the question.

Some sources refer to the problem of **Doubling the Cube** as **duplicating the cube**.

However, the position taken by $\mathsf{Pr} \infty \mathsf{fWiki}$ is that **duplication** can also mean **making an exact copy of**, which could cause misunderstanding.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic of Shape: Problems for the Greeks - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**duplication of the cube**