Delian Cube Doubling Problem

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The Delian Cube-Doubling Problem: Feel the Thrill Now. This is a time-honored challenge that may look straightforward at first glance, but it's actually a captivating math problem spanning from 1D to 3D. It's been proven impossible to double the volume of a cube using an unmarked straightedge and compass. However, with a marked ruler, one can construct the edge of such a doubled cube and thus build the entire cube. Choose your perspective: either Version A or Version B, depending on how you look at it. **Version A:** The whole cube, including its walls, is counted as the volume. **Version B:** Only the interior (capacity) of the cubes is counted as the volume, excluding their walls. The base provides a setup for curious minds to prove that the edge of the doubled cube is the cubic root of 2. It's slightly tricky; look up the Theorem of Menelaus to see how it's done. I won't spoil the fun here. Have fun exploring math and playing with numbers! References: 1. https://en.wikipedia.org/wiki/Doubling_the_cube 2. Dörrie, Heinrich. (1965). 100 Great Problems of Elementary Mathematics: Their History and Solution. (David Antin, Trans.). New York, NY: Dover (Original work published 1958).