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From: Archimedes Plutonium on 14 Jul 2010 15:57
Zugswang is easily seen in the picture proof of Pythagorean theorem
where no words
are needed to make the proof but only a picture of 3 squares resting
on the sides of a
right triangle, and with the other attending pictures.

But my proof that No Odd Perfect Number exists is another Zugswang
proof. It forces
without question the conclusion.

All even perfect numbers start out their accounting with a 50% fill
and then proceed to
only have to add another 50% in combination.

6 is perfect because 50% + the combo of 1/6 +2/6 gives the other 50%

But an odd number can only start filling with 1/3 and can only hope to
receive two more
1/3 combos to make 100%. Here is the Zugswang, or zugzwang, In order
to get the other
two 1/3 combos, you end up with 1/3 + 2/3combos and it is that "2" in
the numerator
which means the odd number was not odd in the first place but was
even.

So that is why mathematics cannot have an Odd Perfect Number (other
than 1).
The proof forces the conclusion and we do not have to go searching
through the proof to
be convinced.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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