The Delian Cube-Doubling Problem: Now You can Feel it.
This is a classic problem! It looks pretty simple; but it is a fascinating math problem, stretching from 1D through 2D to 3D.
It is proven impossible to double the volume of a cube using (unmarked) straightedge and compass. However, with a marked ruler, one can construct the edge of such a doubled cube and thus the whole cube.
Depending on your perspective, please choose either one of the following models.
Version A: The whole cube, including the walls, is counted as the volume.
Version B: The interior (capacity) of the cubes is counted as the volume, excluding the walls.
The base has the setup for the curious mind to prove that the edge of the doubled cube is the cubic (third) root of 2. It is slightly challenging; please look up the Theorem of Menelaus. I am not going to ruin the fun here.
Have fun and play with math!
Dörrie, Heinrich. (1965). 100 Great Problems of Elementary Mathematics: Their History and Solution. (David Antin, Trans.) . New York, NY: Dover (Original work published 1958).
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