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Delian Cube Doubling Problem

77621d171ae8d68dccb3981ac03649fc_preview_featured.jpg Delian Cube Doubling Problem
dbee0ed917b6d246c1d24280bbc17880_preview_featured.jpg Delian Cube Doubling Problem
cube_doubling_Exterior_Vol.stl Delian Cube Doubling Problem
cube_doubling_Interior_Vol.stl Delian Cube Doubling Problem
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Creation quality: 5.0/5 (1 vote)
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  • cube_doubling_Exterior_Vol.stl
  • cube_doubling_Interior_Vol.stl

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Publication date 2018-07-12 at 08:37
Design number 28463
LGBU

LGBU

3D printer file info

3D model description

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!

References
https://en.wikipedia.org/wiki/Doubling_the_cube

Dörrie, Heinrich. (1965). 100 Great Problems of Elementary Mathematics: Their History and Solution. (David Antin, Trans.) . New York, NY: Dover (Original work published 1958).

3D printing settings

Rafts:

No

Supports:

No

Resolution:

0.15-.2mm

Infill:

5-20%

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