# I'm pretty sure they got something wrong on Geometry

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 697488.  Thu Apr 15, 2010 10:09 pm On the show, Stephen Fry said that the white square appeared in the triangle due to the hypotenuse of the two smaller triangles not being straight. While they weren't straight, I am almost 100% sure that is not the case. The reason why the white square appears is because of the smaller shapes being used to make the bigger triangle. They even showed on the screen how the square appears yet still said it was due to the hypotenuse.

697505.  Fri Apr 16, 2010 1:30 am

No, TheBorzoi - the show was right on this occasion. Here's the explanation from Stephen's notes:
 Quote: Curry’s Paradox This is a type of dissection paradox, which works because the hypotenuse isn’t actually straight in either picture; in one of them it bends inwards, in the other outwards, the reason being that the blue triangle has a ratio of 5:2, while the red triangle has the ratio 8:3, and these are not the same - so the two triangles are not ‘similar’. The actual area of the component shapes is 32.5 sq units, whereas the two “assembled” versions are 33 and 32 respectively. The puzzle was invented by a New York City amateur magician Paul Curry (1917 - 1986) in 1953, but the principle of a dissection paradox has been known since the late 18th century.

 697665.  Fri Apr 16, 2010 9:22 am I understand that but even if the hypotenuse was straight, the white square would still be there.

697673.  Fri Apr 16, 2010 10:02 am

 TheBorzoi wrote: I understand that but even if the hypotenuse was straight, the white square would still be there.
#
If you can post a working example with a straight and continuous hypotenuse I'd love to see it.

BugBear

 697689.  Fri Apr 16, 2010 10:33 am I just tried drawing it and realised that I understood it wrong. I thought he meant that the hypotenuse in the smaller triangles were slightly curved but after trying to the shape I realised he meant that the angles of the two hypotenuse are different making the hypotenuse of the larger triangle bent.

697691.  Fri Apr 16, 2010 10:39 am

 TheBorzoi wrote: I just tried drawing it and realised that I understood it wrong. I thought he meant that the hypotenuse in the smaller triangles were slightly curved but after trying to the shape I realised he meant that the angles of the two hypotenuse are different making the hypotenuse of the larger triangle bent.

Bingo!

BugBear

 697697.  Fri Apr 16, 2010 10:48 am Two fat ladies, 88!

697755.  Fri Apr 16, 2010 2:27 pm

...you and yer mother.

 697795.  Fri Apr 16, 2010 4:53 pm I'm only a lady on the weekends!

 697797.  Fri Apr 16, 2010 4:59 pm Yeah, he's a complete slut during the week.

 697821.  Fri Apr 16, 2010 8:18 pm I thought he meant there was a popular beat combo called "the weekends" and ... oh never mind

 698192.  Sat Apr 17, 2010 1:07 pm So the son of the squaw on the bent hippopotamus was not equal to the sons of the squaws on the other two hides.......?

 712144.  Sun May 23, 2010 2:59 pm I was wondering if any other QI detectives noticed the other 'deliberate mistake' in this section?

712145.  Sun May 23, 2010 3:05 pm

 Prolekult wrote: I was wondering if any other QI detectives noticed the other 'deliberate mistake' in this section?

Is it that Mr. Fry actually says "the hypotenuse is curved" when it's not. It's just the two are at slightly different angles. Thus, making it not a curve, but a bend at best.

 712146.  Sun May 23, 2010 3:10 pm no, that's not what I had in mind, although I must say i didn't really get the ratios bit, if only the hypotenuse were different wouldn't the ratios be the same?

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