# The Naked Scientists Forum

### Author Topic: How Can This Be ?  (Read 2440 times)

#### neilep

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##### How Can This Be ?
« on: 08/09/2008 13:38:03 »
As a sheepy, I am of course always fascniated by spaces within triangles but this old one has always confused me...

Is it possible, to explain , in a  very laysheep way, why moving those sections creates a space whereas before there was none  ?

ta

Neil

#### Carolyn

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##### How Can This Be ?
« Reply #1 on: 08/09/2008 14:20:51 »
On the long side of the triangle, the angle is a little different.  The difference is very small, but enough that when you rearrange the pieces, there's a little more space in the second triangle.

If you look closely at the squares on the long side, you can see the difference in the sizes of the two triangles.

#### Evie

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##### How Can This Be ?
« Reply #2 on: 08/09/2008 19:39:50 »
Carolyn is right. This is an optical illusion and the red and green triangles have a very slightly different angle to them. Here's a link to an animation where they tell you the answer at the bottom:

http://www.michaelbach.de/ot/ang_trianglePuzzle/index.html
« Last Edit: 09/09/2008 21:38:29 by Evie »

#### neilep

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##### How Can This Be ?
« Reply #3 on: 08/09/2008 19:49:39 »
On the long side of the triangle, the angle is a little different.  The difference is very small, but enough that when you rearrange the pieces, there's a little more space in the second triangle.

If you look closely at the squares on the long side, you can see the difference in the sizes of the two triangles.

Thanks Carolyn,

I do find it hard to see the difference but apprecaite that ewe can !

Thanks very much

#### neilep

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##### How Can This Be ?
« Reply #4 on: 08/09/2008 19:50:52 »
Carolyn is right. This is an optical illusion and the red and green triangles have a very slightly different angle to them. Here's a link to an animation where they tell you the answer at the bottom: http://www.michaelbach.de/ot/ang_trianglePuzzle/index.html/

Thank Evie

I'm afraid your link doesn't work but believe you and Carolyn that it is then an optical illusion !

Thanks again

#### LeeE

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##### How Can This Be ?
« Reply #5 on: 09/09/2008 17:54:05 »
Concerning the two triangles (both right angled), one of them is 3/8 and the other is 2/5.

For the angle between the hypotenuse and the base...

ATan(3/8) = 20.55604522
ATan(2/5) = 21.801409486

#### Evie

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##### How Can This Be ?
« Reply #6 on: 09/09/2008 21:39:29 »
I fixed the link (I think). Also, if you watch that animation back and forth, you can see where the two triangles don't exactly line up.

#### The Naked Scientists Forum

##### How Can This Be ?
« Reply #6 on: 09/09/2008 21:39:29 »