My challenge to the forum

I'm doing some reading on the Paris Peace Negotiations and the many problems they had getting a table that suited all sides. While there were four parties in the negotiations, not all parties were considered as equals by everyone so choosing how to sit the parties was problematic.

The Danish mathematician and designer Piet Hein proposed a super-elliptical table with golden section proportions – neither square nor round but midway between the two that ‘would allot the two major parties 100 inches to every 6.18 for the two minor parties all the while suggesting sovereignty with alliance’ (technically speaking this table would have a perimeter that satisfied the formula: x2.5+[y/a]2.5=1 where a=[.5][√5-1]). R.

Taking the information contained in the paragraph above, is it possible to transform the math into an illustration? I'm curious to see the illustration but even more curious on how it might be done.

I think it's this, although it seems a little oblong:

Sorry that the ends aren't filled in, but I haven't been able to draw a fully closed figure yet, so any attempt to fill it fills the entire rectangle.

Also note that the formula is:
x^(5/2) + (y / ( (sqrt(5) - 1) / 2) )^(5/2) = 1
Note that 1 / (sqrt(5) - 1) / 2) = (sqrt(5) + 1) / 2, so this can be rewritten as:
x^(5/2) + ((sqrt(5) + 1) / 2 y)^(5/2) = 1
which is x^(5/2) + ((sqrt(5) + 1) / 2)^(5/2) y^(5/2) = 1
which is x^(5/2) + sqrt(22 + 10 sqrt(5)) / 2 y^(5/2) = 1
Note that sqrt(22 + 10 sqrt(5)) / 2 is just under 10/3

Thank you. So am I to understand that the ends of the table should be rounded and red? Almost like a surfboard overall. I finally get the inside joke from Apocalypse Now.

Quote: billryan

Thank you. So am I to understand that the ends of the table should be rounded and red? Almost like a surfboard overall. I finally get the inside joke from Apocalypse Now.
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Yes.

I have a feeling whoever wrote the article may have gotten the formula wrong. If you replace (sqrt(5) - 1)/2 with (sqrt(5) + 1)/2, the table looks like this:

I remember reading this issue of Life from 1966.

Thank you, although the picture leaves me almost as confused as before.

I think what he was going for was that the US and North Vietnamese would be sitting in the middle where the table was slightly wider and the other parties would be on the same side of the table but in a slightly inferior position.
They couldn't use a round table, where everyone was equal because the South Vietnamese and the Viet Cong refused to recognize each other. South Vietnam wanted a triangular table, but the North wanted a square with each party as equals .
The various sides couldn't even agree that there were four parties negotiating so they simply referred to negotiators as "from our side" and "from your side"