Guess where is the missing square

[BobTheCrate]

Easier to use a dodgy version of Paintshop to overlay the top triangle over the bottom triangle.

[Churchill]

Easier to use a dodgy version of Paintshop to overlay the top triangle over the bottom triangle.

Bob, you should know better than to try and have a debate with Threaded the mighty Prince of Bulltulip!

[BobTheCrate]

The mighty prince of bulltulip

An impressive title indeed.

Clearly I didn't know any better and temporarily hold my head down in embarassment.

[BobTheCrate]

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.

The areas do match the maths. That is, the areas of each coloured shape.

Tell you what.

1. Use something like PSP and re-create one of the triangles for yourself complete with coloured shapes. It doesn't matter which triangle you re-create.

2. Then cut out each coloured shape.

3. Then rearrange your shapes to the same pattern as you see in the bottom triangle.

It'll take you no more than 5 mins to prove it to yourself and solve the mystery. No gradient mis-match, no optical illusion, no image difference - just a simple jigsaw re-arrangement that creates a space in the jigsaw which people mistakenly read as a square.

[Harrysp]

So There :-D

In the first triangle, moving from left to right, you move at one
slope (3/8), and then switch to a steeper slope (2/5). This means that
the 'hypotenuse' is not actually a straight line, but in fact is
slightly concave. In the second triangle, the situation is reversed:
you switch from a steeper slope to a gentler one, which makes the
'hypotenuse' slightly convex.

In fact, then, neither of the 'triangles' is really a triangle at all,
but a quadrilateral in which one of the angles is nearly 180 degrees.
The thickness of the line is used to mask the change in slope; but the
difference between the convex and concave 'hypotenuses' is the area of
the white square in the bottom triangle.

[oliver]

The white square in the bottom triangle is not a square - it is a blank space[/b][/i] created by a mismatch in rearranging pieces of a jigsaw.

The square is not a square? LOL! What is it - a circle? A trick of the light?

The bigger boys have told you how this trick works (the overall shape is actually not a triangle) but what is funny is that not only could you not work this out for yourself but even when people explain it you still stick to the "I don't understand it therefore it is a 'jigsaw trick' (whatever the hell that is) theory".

[threaded]

I have a lovely book full of optical illusions like this.

[BobTheCrate]

Charming.

Now explain Oliver why it is that you can re-create the bottom triangle and shapes identically, using the shapes from the top one ?

Explain why the top triangle overlays the bottom triangle exactly. How is that possible if the hypotenuse of each are bending in different directions or that both shapes are not even triangles but different shapes from one another altogether.

Seeing as though you are so clever and know it all. Explain away those little fundamental chestnuts.

For someone who doesn't recognise a simple jigsaw puzzle, you're inviting a great deal of egg on your face by accusing others of being thick.

The square is not a square? LOL! What is it - a circle?

No, I told you already. You don't hear so good so I'll tell you again. It is a 'space', a 'blank'.

http://www.rupoint.co.uk/attachment....id=10425&stc=1

[BobTheCrate]

Anyone interested in proof this is a jigsaw puzzle, try either of the 2 methods below.

Method 1

1. Make a copy of the illustrated top triangle.

2. Using a paint pgm, cut out the coloured shapes.

3. Re-arrange those shapes to match what you see in the bottom triangle.

See ?

You have re-created the bottom triangle (incl the space) identically by using exclusively all the coloured parts of the top triangle.

How could you have done that if they were different triangles or different shapes altogether ?

OR

Method 2 (If you don't trust the optics of the illustrated triangles)

1. Create your own version of the top triangle with the same coloured shapes within it.

This way you can guarantee you're using precise shapes and not optical illusions or different shapes, thickness of lines or whatever.

2. Again, cut out the coloured shapes.

3. Re-arrange those shapes as you see them in the bottom triangle.

There ... proof it is a jigsaw puzzle.

http://www.rupoint.co.uk/attachment...tid=10425&stc=1

[AtW]

Gee Bob, since when you had that burning desire to prove you always right?