True dat!

...from cg.com's Quote of the Day series:

Bishops move diagonally. That's why they often turn up where the kings don't expect them to be. --- Terry Pratchett

Well, now we know why. :p

Like the Reutersvärd / Penrose / Escher triangle.

1. e4 e6 2. d4 d5 3. Nc3 Nf6 4. Bg5 dxe4 5. Nxe4 Be7 6. Bxf6 Bxf6 7. Nf3 Nd7 8. Qd2 O-O 9. O-O-O b6 10. Bc4 Bb7 11. Rhe1 Bd5 12. Bxd5 exd5 13. Ng3 g6 14. Ne5 Nxe5 15. dxe5 Bg7 16. f4 c6 17. Ne2 Qd7 18. Nd4 c5 19. Nf3 Rad8 20. Kb1 Rfe8 21. Qd3 Qg4 22. g3 b5 23. Qb3 Bf8 24. Nd2 a6 25. Qf3 Qh3 26. Nb3 d4 27. Nd2 c4 28. Ne4 Be7 29. Nf2 Qe6 30. Re4 Bc5 31. Ng4 f5 32. Nf6+ Qxf6 33. exf6 fxe4 34. Qg4 e3 35. f5 Kf7 36. Qh4 e2 37. Qxh7+ Kxf6 38. Qxg6+ Ke5 39. Re1 d3 40. cxd3 cxd3 41. f6 Be3 42. f7 Rf8 43. Qh5+ Kd6 44. Qf5 d2 1/2-1/2

<Chess players are madmen of a certain quality, the way the artist is supposed to be, and isn't, in general.>

– Marcel Duchamp

Ah, *that* triangle. In hyperbolic space where the angles never sum to 180 degrees? Or pi, even.

I know many chipmonks socially and lemme tell you, they ... oh, you said 'chipmunks'. That's different. I have no data on their virility. I guess the alpha male chipmunks have some, unless they've been selected for wimpery.

Yup. That's what comes of switching from cutting corners of triangles, to cutting corners in communication. :p

It would probably be more precise - if less catchy - to say something like 'an infinite number of two-dimensional depictions (relying on optical illusions), of realistically impossible figures (or at least impossible to duplicate in three-dimensional space with the "simplicity" implied by their 2-D representations), is possible'.

But that's even more convoluted than one of those triangles, and/or a Möbius strip - and considerably less "elegant". Alternatively, one could just say something like: 'these optical illusion tricks are possible for other figures besides triangles'. Arguably, such a statement might be too simple, straightforward, and transparent, for that page... or this page, for that matter. ;)

<One can, of course, draw a triangle with three right angles on the surface of a sphere ...>

Well yes, but isn't that sortof a copout, in a way, too?

Are you familiar with the career and games of <Vera Menchik>?

Why do you think so few people know about her compared to the <Polgars>?

Yes, Jessica, I've noticed her page some 4 years ago.

<Why do you think so few people know about her compared to the <Polgars>?>

That question can be broken down into two timeframes:

(1) Why did so few people know about her back when she was alive and active;

(2) Why do so few people know about her now.

The answer to (1) is that I have no idea just how many people knew about her back then - she may have been quite well known, for all I know - but then again, considering that even Fischer and Kasparov are hardly known outside of chess circles even today, probably not.

The answer to (2) may, sadly enough, have something to do with the fact that she can't be considered very attractive by present beauty standards (like Kosteniuk for counterexample), plus she has the disadvantage of not being involved in current tournaments and news (like the Polgars), plus see answer (1).

Thanks for that informative and thoughtful response.

I agree that in "general public terms" the fact that nobody really cares that much about Chess Masters would be a factor- in terms of chess circles, however, in her time she was well known by the "major players" because of her participation in International Tournaments. Her good friend <AA Alekhine> praised her play at <Karlsbad 1929> in an article for the New York Times, even though she managed just two wins and three points at that event.

I think your point about chess beauty is, sadly, accurate. For example, in my research I found several photos of <Sonja Graf>, her great German contemporary, in newspapers. <Sonja> looked like <Demi Moore>.

But no newspaper photos of <Vera> to be found.

And yes the appalling circumstances of her death- her whole family wiped out at once in the Blitz- is horrifying.

As is the <Jessie Gilbert> story.