# The vanishing space....???...



## peejay (May 10, 2005)

Where did the space come from?










pj


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## DABurleigh (May 9, 2005)

Very good!

It took a worryingly long time to solve it.

Dave


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## arrow2 (May 9, 2005)

Someone please put me out of my misery!!!

Kevin


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## 95384 (Jun 9, 2005)

look at the coordinate x=5 y=2 - on pic one it is slightly less than2. On pic 2 it is exactly 2. therefor the hypotenuse on pic one is slightly lower, so the entire triangle area is slightly less. The other square is made from the difference


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## badger (May 9, 2005)

look at the coordinate x=5 y=2 - on pic one it is slightly less than2. On pic 2 it is exactly 2. therefor the hypotenuse on pic one is slightly lower


Der.......yeh ....right.........


SO where did the space come from???.


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## peejay (May 10, 2005)

Err...

Confession time, pinched this from another site and theres no solution for it there either.

bb695's explanation is clear as mud to me as well!

DABurleigh wrote'



> It took a worryingly long time to solve it


Me too Dave, in fact very, very worryingly as I haven't a clue :roll:

pj


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## 88962 (May 10, 2005)

Now how do I explain my theory on 'paper' :idea: . If you put a ruler along the top diagonal edge of each image you'll find that the top one is concave and the bottom one convex. This also shows as if you put a ruler along along the diagonal blue line on the top image it finishes almost a square short on the red base line. Seems to be nothing scientific - just bending the rules - or lines. 
Is it my eyes, the fact that I don't have a flat screen or can anyone else confirm this theory?


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## Motorhomersimpson (May 9, 2005)

Nice one Pete,

Can never figure these out, the only space I'm sure about is the space between my ear's. :lol: :lol: 

bb695, thats like looking at my daughters work, (she's studying A level maths), straight over my head I'm afraid. :lol: :lol: 

MHS....Rob


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## DABurleigh (May 9, 2005)

Every coloured shape - red, blue, yellow, green - is individually EXACTLY the same size and shape on both top and bottom arrangements.

However, the overall assembled shapes are NOT triangles, because the "slopes" of the red and blue triangles are DIFFERENT. Swap the order of these red and blue triangles and in one case, these different slopes form a convex "hypotenuse", in the other, a concave "hypotenuse".

If one overall shape were overlaid on the other, the difference would be a very long, very thin "diamond" along the "hypotenuse". The area of this diamond is equivalent to the one square (with the questionmark in).

Numerically, as the area of a triangle is half base times height, the areas are:
Red: 12
Blue: 5
Yellow: 7
Green: 8

This adds up to 32, the area of the top shape. Note if this WERE a triangle, it SHOULD have an area 1/2 * 13 * 5 = 32.5, so the "concave" assembly has robbed 0.5 of a square.

Conversely the bottom shape is, of course, area 32+1 = 33, as the "convex" assembly has added 0.5.

QED

Dave


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## 95384 (Jun 9, 2005)

Cheers Dave - sometimes I forget that no every poor soul in the world had to do a maths degree :lol: 

In basic terms - the shapes are the same shape and size, but the triangles are different. Sort of like comparing a lorry with a bicycle, but in this case the difference is so minor that it is like comparing a lorry with a slightly smaller lorry


OK - Maybe tomorow I will call in before the pub and explain it properly 8O


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