comment on comment

My thanks to Keira, who commented on the trisection entry (see below). I wanted to reply to her points, but since it is either (a) devilishly difficult to contact her, (b) impossible, or (c) I'm too stupid and/or impatient to hunt for a real contact - I'll assume the last option - I'd like to comment right here.

For your convenience, I'll copy her comment right here:

Sorry, you certainly cannot go by eye or compass alone; you have to do the trigonometry to get actual measurements. The method you show, for example, on a 60° angle, yields two 19.792...° angles and one 20.103...° angle. That's not even very close.

I wanted to thank her personally for pointing this out to me, and ask for an explanation of her method. The fact that I'm asking for that betrays my ignorance of trigonometry, and I won't hide it. But given a little time and maybe a dash of assistance, I think I can understand it, and thus get a better idea of the situation.

To reply: I know that eyeballing it is not kosher for the game of trisection; I also realize that the compass alone is insufficient. But any particular drawing will be imperfect, even a simple bisection will be off a little. The reason for this, of course, is that there are deviations too small to be detected by the naked eye. And in this case, we are facing the venerable dictum that trisection cannot be done in principle.

Jim Loy's website - been there, done that, got the T-shirt.

Now I'm not saying that Wantzel's proof is wrong; what I'm saying is that here is a suggestive method for doing the impossible, and if it indeed works in principle - and sufficiently well in fact - then it's worth inquiring into the errors of the proof. I do not have the mathematical know-how to do this; maybe someday, but not right now.

None of this would be to slag Wantzel. I'm neither trying to show anyone's stupidity nor my own superiority. I'm simply asking: please show me that this method is in principle wrong without referring to Wantzel's proof. If the method is flawed, show the flaw - don't dismiss it out of hand. There's a whole book devoted to this sort of thing: A Budget of Trisections by Underwood Dudley. It does not include this method, probably because the author never saw it. And no wonder - it was printed in a small, now-defunct journal in the '70s. All I want is something of a similar nature.

You know, this is just a case study of the value of heresy. If something is true, it should be able to withstand challenges; but if it's not challenged, how can we know its strength? That is all. Peace out.