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Chronos
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 Re: More Lies   « on: Apr 9th, 2003, 7:34pm » Quote Modify

Note that diagram is not quite to scale, so inferrences made from the diagram are not necessarily accurate.  In particular, point B is actually on the other side of segment PD, so angle BDC is actually equal to the difference of PDC and PDB, not the sum.  So the math all works out.
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Icarus
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 Re: More Lies   « Reply #1 on: Apr 9th, 2003, 8:33pm » Quote Modify

Thank you! I first saw this one in college (an unfortunately long time ago for me) and have racked my brains trying to remember how it went so that I could post it here.

I came across it in a collection of articles from "The Journal of Irreproducible Results". The variation in the article proved that all obtuse angles were congruent to a right angle (angle ABD is congruent to angle CAB), and claimed it was the "Lost theorem of Euclid". The article went on to claim that the earliest fragments of of Euclid's Elements ever found had the later theorems numbered 1 higher than in the version seen today, but the portions containing the extra theorem were lost. Scholars had speculated as to what the theorem was, and why it was removed, until a copy was finally found. At that time it was realized the theorem had been deliberately suppressed as soon as its extraordinary military applications became apparent. (After all, if all obtuse angles are congruent to a right angle, it quickly follows that all angles are equal, and therefore moment of inertia is simply a matter of "reference frame", or as the Greeks put it: "place to stand"). The article went on to speculate about what Archimedes really meant by "Give me but a place to stand, and I shall move the Earth!", and whether certain astronomical anomalies might date back to his time.
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"Pi goes on and on and on ...
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I wonder: Which is larger
When their digits are reversed? " - Anonymous
redPEPPER
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 Re: More Lies   « Reply #2 on: Apr 12th, 2003, 7:30am » Quote Modify

A picture being worth a thousand words:

The two triangles are indeed equal.  But as chronos said, B is on the left of PD, not on the right.  So the angle BDP is not a part of BDC.  The lie was in the last sentence of the original text, when you discreetly assume (without even wording it) that BDP + PDC = BDC.
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Icarus
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 Re: More Lies   « Reply #3 on: Apr 12th, 2003, 5:34pm » Quote Modify

I thought you knew it too. When I saw the version I mentioned earlier, I finally had to plot it using cartesian coordinates in order to find the problem.

I posted the article with a challenge to find the error on my office door for about 5 years at college (I was a TA as a grad student). No one ever said a word to me about it.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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