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I'm pretty sure they got something wrong on Geometry

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TheBorzoi
697488.  Thu Apr 15, 2010 10:09 pm Reply with quote

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.

 
Flash
697505.  Fri Apr 16, 2010 1:30 am Reply with quote

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.

 
TheBorzoi
697665.  Fri Apr 16, 2010 9:22 am Reply with quote

I understand that but even if the hypotenuse was straight, the white square would still be there.

 
bugbear
697673.  Fri Apr 16, 2010 10:02 am Reply with quote

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

 
TheBorzoi
697689.  Fri Apr 16, 2010 10:33 am Reply with quote

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.

 
bugbear
697691.  Fri Apr 16, 2010 10:39 am Reply with quote

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

 
CB27
697697.  Fri Apr 16, 2010 10:48 am Reply with quote

Two fat ladies, 88!

 
Bondee
697755.  Fri Apr 16, 2010 2:27 pm Reply with quote

CB27 wrote:
Two fat ladies


...you and yer mother.

 
CB27
697795.  Fri Apr 16, 2010 4:53 pm Reply with quote

I'm only a lady on the weekends!

 
Sadurian Mike
697797.  Fri Apr 16, 2010 4:59 pm Reply with quote

Yeah, he's a complete slut during the week.

 
bobwilson
697821.  Fri Apr 16, 2010 8:18 pm Reply with quote

I thought he meant there was a popular beat combo called "the weekends" and ... oh never mind

 
mckeonj
698192.  Sat Apr 17, 2010 1:07 pm Reply with quote

So the son of the squaw on the bent hippopotamus was not equal to the sons of the squaws on the other two hides.......?

 
Prolekult
712144.  Sun May 23, 2010 2:59 pm Reply with quote

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

 
TheBorzoi
712145.  Sun May 23, 2010 3:05 pm Reply with quote

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.

 
Prolekult
712146.  Sun May 23, 2010 3:10 pm Reply with quote

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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