Guess where is the missing square

[The Lone Gunman]

I think this is an optical illusion, vision trick. But a trick

The straight lines are not actualy straight. The pieces do not actualy match up in size. Tiny differences in sizes adds up to one whole square.

[DimPrawn]

hyperD is spot on. The lines are not straight on the hypotenuse. On one it bows in on the other it bows out. Enough to make up 1 square in area.

[Rebecca Loos]

very disappointing. I thought it was something a bit more clever than that
Oh well
Bloody Russians

[BobTheCrate]

Solution: There is no missing square

Yep fascinating puzzle.

Those who thought it is something to do with the gradient are way off the mark. Both hypotenuse run straight and parallel.

Proof. You can indeed rearrange the shapes from the top triangle and position them as per the bottom triangle and reproduce the supposed white square.

So it is nothing to do with gradient and it is no optical illusion. It is a trick.

It is merely a clever jigsaw mismatch whereby the pieces are rearranged leaving two pieces (green & tan) that will will not meet. I suppose the illusion is that people 'read' the blank space as a white square when infact it is not a square at all. It is just a blank space.

[Churchill]

Wrong!! The gradient of the small green triangle is 40% (2/5), but the gradient of the larger red triangle is 37.5% (3/8).
Just count the little squares......

I thank you very much! We Dogs have bloody good eyes.

[BobTheCrate]

ABC angles - gradient is identical

Wrong!! The gradient of the small green triangle is 40% (2/5), but the gradient of the larger red triangle is 37.5% (3/8).
Just count the little squares......

The number of little squares are different because the red & green triangles are different sizes. But the ABC angles of all triangles are identical and proves the gradient is the same. Additional proof is that the hyp of both triangles run parallel to one another. The ABC angles of both parent triangles are also identical.

You can overlay the top triangle over the bottom triangle exactly. The lengths of hyp, opp and adj match exactly as do all the ABC angles of the parent and any other smaller triangles.

Take each coloured shape from the top triangle and you can re-arrange them to replicate the bottom triangle ... including the 'space'. This could not be done if the gradients differed.

Again. The white square in the bottom triangle is not a square - it is a blank space created by a mismatch in rearranging pieces of a jigsaw.

[threaded]

Bob: It is a well known optical illusion caused by a bowing of the hypotenuse. Print it out. Check it with a ruler. Live with it.

[The Lone Gunman]

Bob, I think you are right about the angles and stuff, but the areas dont match the maths, do the maths. The area of the big triangle is at least 1/2 a square more than the parts filling it. The thickness of the lines accounts for the other half square.

[BobTheCrate]

Bob: It is a well known optical illusion caused by a bowing of the hypotenuse. Print it out. Check it with a ruler. Live with it.

If that is the case threaded. Please explain :-

i) Why the top triangle overlays the bottom identically ?

ii) Why the individual coloured shapes in the top triangle can be rearranged to reproduce the bottom triangle identically ?

[threaded]

You have a pair of dodgy scissors?