Can anybody solve this?
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Ok here is an illusion: http://www.briandela.com/files/picture.gif[^] Regards, Venet. Donec eris felix, multos numerabis amicos.
Hint: look very closely at the hypotenuses (wtf is the plural of hypotenuse?)
Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokingly -
Ok here is an illusion: http://www.briandela.com/files/picture.gif[^] Regards, Venet. Donec eris felix, multos numerabis amicos.
Yes. ;P
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Ok here is an illusion: http://www.briandela.com/files/picture.gif[^] Regards, Venet. Donec eris felix, multos numerabis amicos.
Solution please! - Before I go insane!!! :eek: John www.silveronion.com[^]
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Hint: look very closely at the hypotenuses (wtf is the plural of hypotenuse?)
Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokingly -
Ok here is an illusion: http://www.briandela.com/files/picture.gif[^] Regards, Venet. Donec eris felix, multos numerabis amicos.
Basically, it's Pythagorus' theorem. The hypotenuse is constructed of the red and green triangles and thus stays the same length. The side opposite to the hypotenuse (the bottom side) is constructed of 13 boxes in the first triangle, but only 12 in the second triangle. The remaining side is constructed of 5 blocks in both triangles. So, the only difference is 1 missing block in the second triangle. Triangle 1 agrees to Pythagorus' triangle theorem which states that the square of the hypotenuse is equal to the sum of the squares of the other sides in a right angle triangle (side note: this is reinforced by the sine rule). Basically: The triangle's hypotenuse = Sqrt((13^2) + (5^2)) = Sqrt(169 + 25) = Sqrt(194) = 13.928 The hypotenuse is the same in triangle 1 and triangle 2 because no shapes have changed in size - they have just been re-arranged. As a result of the arrangement of blocks in the second triangle, the length of the bottom edge becomes 12 blocks. 13.928 is not equal to Sqrt((12^2) + (5^2)) = Sqrt(144 + 25) = Sqrt(169) = 13 Simply: if the bottom set of blocks was compressed to form no gaps, the hypotenuse would be 13 blocks instead of 13.928. That's impossible because none of the shapes have changed in size. So to compensate for this, a gap of 1 block has been left to make the length of the bottom side of the triangle effectively 14 blocks. I need to learn how to explain things clearly. Bah. ;) -Chris "Apparently I'm not supposed to say that infront of customers" Pointy Haired Boss, Dilbert
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Ok here is an illusion: http://www.briandela.com/files/picture.gif[^] Regards, Venet. Donec eris felix, multos numerabis amicos.
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Basically, it's Pythagorus' theorem. The hypotenuse is constructed of the red and green triangles and thus stays the same length. The side opposite to the hypotenuse (the bottom side) is constructed of 13 boxes in the first triangle, but only 12 in the second triangle. The remaining side is constructed of 5 blocks in both triangles. So, the only difference is 1 missing block in the second triangle. Triangle 1 agrees to Pythagorus' triangle theorem which states that the square of the hypotenuse is equal to the sum of the squares of the other sides in a right angle triangle (side note: this is reinforced by the sine rule). Basically: The triangle's hypotenuse = Sqrt((13^2) + (5^2)) = Sqrt(169 + 25) = Sqrt(194) = 13.928 The hypotenuse is the same in triangle 1 and triangle 2 because no shapes have changed in size - they have just been re-arranged. As a result of the arrangement of blocks in the second triangle, the length of the bottom edge becomes 12 blocks. 13.928 is not equal to Sqrt((12^2) + (5^2)) = Sqrt(144 + 25) = Sqrt(169) = 13 Simply: if the bottom set of blocks was compressed to form no gaps, the hypotenuse would be 13 blocks instead of 13.928. That's impossible because none of the shapes have changed in size. So to compensate for this, a gap of 1 block has been left to make the length of the bottom side of the triangle effectively 14 blocks. I need to learn how to explain things clearly. Bah. ;) -Chris "Apparently I'm not supposed to say that infront of customers" Pointy Haired Boss, Dilbert
Now that I look at the picture again, it seems that the illusion is that the second arrangement of partitions appears to occupy less area than the first arrangement. Area of First Shape ((5 * 13) / 2) = 32.5 blocks Area of Second Shape ((3 * 7) / 2) = 10.5 blocks (((2 + 2) * 1) / 2) = 2 blocks (((3 + 5) * 5) / 2) = 20 blocks Total area = 10.5 + 2 + 20 = 32.5 blocks I think the reason it looks strange is because our brain tries to interpret the partitions as an individual object. The second shape is not a triangle, so we shouldn't really interpret it as one. The illusion just doesn't exist if the picture is changed to:
http://www.aeroglade.net/cp_temp/picture.gif
However, it is -exactly- the same concept! :) -Chris "Apparently I'm not supposed to say that infront of customers" Pointy Haired Boss, Dilbert
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Ok here is an illusion: http://www.briandela.com/files/picture.gif[^] Regards, Venet. Donec eris felix, multos numerabis amicos.
The picture is not a triangle. If you look at the ratio of sides, the small triangle is 5:2 where the big one is 8:3. So, the hypothenuse is not a straight line.
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Now that I look at the picture again, it seems that the illusion is that the second arrangement of partitions appears to occupy less area than the first arrangement. Area of First Shape ((5 * 13) / 2) = 32.5 blocks Area of Second Shape ((3 * 7) / 2) = 10.5 blocks (((2 + 2) * 1) / 2) = 2 blocks (((3 + 5) * 5) / 2) = 20 blocks Total area = 10.5 + 2 + 20 = 32.5 blocks I think the reason it looks strange is because our brain tries to interpret the partitions as an individual object. The second shape is not a triangle, so we shouldn't really interpret it as one. The illusion just doesn't exist if the picture is changed to:
http://www.aeroglade.net/cp_temp/picture.gif
However, it is -exactly- the same concept! :) -Chris "Apparently I'm not supposed to say that infront of customers" Pointy Haired Boss, Dilbert
Christopher Davies wrote: The second shape is not a triangle, so we shouldn't really interpret it as one. Since the angles of the red triangle are different than the angles of the dark green triangle they are dissimilar and thus neither "shape" is a triangle.
Work like you don't need the money.
Love like you've never been hurt.
Dance like nobody's watching. -
Ok here is an illusion: http://www.briandela.com/files/picture.gif[^] Regards, Venet. Donec eris felix, multos numerabis amicos.
I just wanted to point out what a great naming convention Brian uses. I mean, picture.gif...that could be anything from porn to well, a shape puzzle. :)
Hawaian shirts and shorts work too in Summer. People assume you're either a complete nut (in which case not a worthy target) or so damn good you don't need to worry about camouflage... -Anna-Jayne Metcalfe on Paintballing
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Hint: look very closely at the hypotenuses (wtf is the plural of hypotenuse?)
Jon Sagara
A bottle a night isn't alcoholism - it's persistence! -- A coworker, jokingly -
I just wanted to point out what a great naming convention Brian uses. I mean, picture.gif...that could be anything from porn to well, a shape puzzle. :)
Hawaian shirts and shorts work too in Summer. People assume you're either a complete nut (in which case not a worthy target) or so damn good you don't need to worry about camouflage... -Anna-Jayne Metcalfe on Paintballing
David Stone wrote: I just wanted to point out what a great naming convention Brian uses. I mean, picture.gif...that could be anything from porn to well, a shape puzzle. It makes you wonder what else he is hiding :suss: Matt Newman Post best viewed with lynx
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"The word hypotenuse comes from Greek, which is a declined language." What? :wtf: Does declined means something special in grammar? or he means that my language is dead? ..and yes, plural of "yptinousa" is "yptinouses". so in english you could say hypotenuses. :) - - - - - - - - - - - - - - - - - - Memory leaks is the price we pay \0 01234567890123456789012345678901234
