One legend
Minos and the royal tomb
In an ancient account, King Minos asks for a cubic tomb to be doubled without losing its form. Doubling every edge seems natural. But does it really double the volume?
A look at the mathematics
Can you double a cube?
A simple question that occupied the greatest minds of humanity for over two millennia, which eventually led to new discoveries in mathematics.
Suppose a cube has side length a. You want to construct another cube with exactly twice its volume.
How long should the new side be?
Another legend
The oracle at Delos
A second story, set on the Greek island of Delos, tells of an oracle asking that Apollo's cubic altar be doubled. The geometric puzzle became known as the Delian problem.
Try it
What does it really mean to double a cube?
The obvious answer is a good place to begin. Is it right?
Questions to follow
Does doubling each dimension really double the volume of a cube? How could you test your answer?
What should the new side length satisfy if the new cube is to have exactly twice the original volume?
What does the cube root of a number mean geometrically? Can you describe it without using a calculator?
If you know the required length algebraically, have you solved the ancient problem? What might “constructing” that length require?
The point is to explore more deeply, as mathematicians from different cultures did for centuries. An innocent-looking question can open doors once unimaginable and lead to entirely new ways of seeing a problem.