The duplication of cube (new solution)

May 02, 2012 22:01

The solution has no possibility of practical application, and that adds the pleasure to it ( Read more... )

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jens_g June 23 2012, 22:18:22 UTC
I had the problem, that I do not see how to construct the angle at the base of the pyramide. However I thought, that things become easier if one simplifies the geometry ( ... )

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jens_g June 23 2012, 22:40:36 UTC
Sorry, 'pooring' needs to be replaced by 'pouring'.

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mos_jkh June 25 2012, 19:38:20 UTC
1. This reversed pyramide without bottom was invented for finding cubic roots (filling its volume by liquid - which volume is equal volume of two cubes - value that we seek - is the side of the square on the upper surface of the liquid in the pyramide ( ... )

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jens_g June 26 2012, 21:10:53 UTC
>(you don't describe any method of finding a cubic root).

Of course, I do not. I am basically doing nothing else but using your method. Rewriting it for myself has clarified the things for me. I am now convinced that one can either use an inverted pyramide or the prisma (put on its tip) in rather equivalent ways.

I am basically using your equations. (I am not sure whether my way to write potencies is generally understood:
a**3 = a * a * a).

The only other difference is, that I replace h in the volume formula in a different way. Thereby you calculate k = SA/L, while I calculate something I should not have called k, but may be q = h/L.

For the pyramide I get h = 3L, which is consistent with k = (9 + 1/2)**1/2.

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