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CEG\'er
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I saw this on another forum, and no one could answer.  I know that it is either a optical illusion, or it is some mathematical answer that i don't understand. I have a couple ideas, but i want to see what you all think
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It's just the way they are stacked. Seems logical to me.
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CEG\'er
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right, but how are they the EXACT same pieces, taking up the same amount of space, just with a hole in it? Logically, it doesn't make sense. How can the same amount of squares take up less room in a triangle that is the same size?
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Well when you swap the 2 triangles it's going to leave a different size square underneath. The L shaped pieces just happen to fit together in an order where a square is missing.
-'96 SE MTX 3L
-'98 SVT 1,173 of 6,535
-'05 Mazda 6s, loaded, g/f's ride
-Need a 96-00 manual on CD? PM or email me
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Do you want the answer, or do you want everyone to guess? 
1999 Sportage 4x4...don't go there, it was free
....______o_o
.../_l l__\____\
..|--l l__----[]\|/[]
.....................oo
=( )_)----( )_)--)_)
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The two triangles have different slopes... 2:5 and 3:8, while in the first setup it appears to make one big triangle, it doesn't the "hypotenuse" isn't a straight line, so I guess you could call it an optical trick.
Add up the individual areas and they are the same, or as Todras said, just look at each piece they haven't changed, it's just a different arrangement.
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you can tell the triangles are two different angles from the second picture...
1999 Sportage 4x4...don't go there, it was free
....______o_o
.../_l l__\____\
..|--l l__----[]\|/[]
.....................oo
=( )_)----( )_)--)_)
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CEG\'er
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Originally posted by SVZETEC:
Do you want the answer, or do you want everyone to guess?
i don't have the answer, but i did have ideas. I showed this to my teacher in my CIS class, and the only thing that we could come up with was the fact that if you put a straight edge up to the monitor, the hypotenuse of the top triangle curves inward, and the hypotenuse on the bottom triangle bulges out. However, many people in the class disagreed that this was enough to make up for the whole square. I just wanted to see if you all had any other opinions, because it is still kinda wierd.
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Visually, the long side(cant remeber the geometrical name, been too long) on the one missing the block crosses the grid at different points...overlaying them in photoshop it's obvious that the line bulges a little...if this is enough to make a whole square of difference, I dont know... 
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Originally posted by spacemonkey:
I saw this on another forum, and no one could answer.
I know that it is either a optical illusion, or it is some mathematical answer that i don't understand. I have a couple ideas, but i want to see what you all think
Both triangles are half of 13x5 or 32.5 square units.
Ok, in the first image, red is 12 square units. (It is 8x3, but cut in half diagonally)
In the second image, red is also 12 square units.
The non-triangle pieces we agree are also the same size in both and occupy individually 7 or 8 square units in each image.
The dark green triangle piece occupies 5 square units in both
examples.
So in the first example.
Red = 12 units
Light Green = 8 units
Dark Green = 5 units
Orange = 7 units
Total space apparently occupied is 32 units, it doesn't quite match the 32.5 units we predicted.
Let's look at the second one.
Same space Red = 12 , Lt Green = 8, Dark Green = 5, Orange = 7 and now white = 1. Total units is 33 again, not exactly what we predicted.
Is it a rounding issue?
TB
"Seems like our society is more interested in turning each successive generation into cookie-cutter wankers than anything else." -- Jato 8/24/2004
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