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Mind f**k Pictures?


Davetrials

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Cant quite remember, but the gridlines arn't stright too. By combining both that and the convex hypotenuse they get a spear square.

Edited by JT!
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The reason that people sometimes find this puzzling is because they start off making an assumption. Often they don't even realize they have made this assumption. The assumption is that we are comparing two triangles, and that they each have the same area. Certainly a quick inspection - helped by the grid - is that the 'triangles' are 13 squares across, and five squares high, and they kind of look the same.

In fact the top triangle is not a triangle at all, it is a tetrahedron. If you look closely along the line of the hypotenuse (the diagonal), you will see that it is not quite straight, it is slightly concave. Why? Well, the dark green triangle is 5 squares across, and 2 squares high. The red triangle is 3 squares high, and should be 7.5 squares across for the hypotenuse to have the same angle to the horizontal. In fact the red triangle is 8 squares across, and the angle of the hypotenuse is slightly shallower that that of the green triangle. Which is why the hypotenuse is not a straight line, when you look closely. The bottom 'triangle' is not a triangle either, it is also a tetrahedron, but now the hypotenuse is slightly convex, since the position of the red and green triangles is now reversed.

Here is an image of the two triangles superimposed, which shows the difference in the two hypotenuse...

IPB Image

The area of the two 'triangles' is actually the same, since it is made up of the same pieces. But because the lower 'triangle' has a 'hypotenuse' that is actually convex, this extra area is the equivalent of one square, which is why the lower shape has a missing square.

(Y)

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Jonathan Trillo = Official Trials Forum Mathematician :turned:

Jonathan Trillo = Good at finding shit on the net.

Made one of those dragons and named him albert. Whats complicated about mountain/valley folds :P it even explains it on the pdf :P

I made one of them ages ago, it's sat on our fridge. They're really freaky. :S

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It's obvious what it means, and there's a picture on the PDF anyway... Not rocket science! I made one, it's very cool, but I find you have to be a long way away for it to work. If you close one eye it works much better, but most people don't do that.

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It says on the pdf to use one eye that way you dont get a 3d perspective on it. Works great about 30cm away from it with one eye closed.

If works with two eyes too if you're far enough away. Or quite close if I take my glasses off :P

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It's obvious what it means, and there's a picture on the PDF anyway... Not rocket science! I made one, it's very cool, but I find you have to be a long way away for it to work. If you close one eye it works much better, but most people don't do that.

i found you had to use one eye but now it works with both eyes open which is quite wierd because it moves all the time now.

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