Guess where is the missing square

[oliver]

What's it to be ? Insults or dialogue ?

Insulting dialogue?

All I am saying is that the same puzzle/effect or whatever you wish to call it, can be easily replicated using a geometrically perfect triangle. Without the use of any curved hypotenuse or visual tricks.

If I cannot persuade you of that and boy I've tried, I fail to see the purpose in continuing if all I get in response are unnecessary insults.

Yes you've tried and tried but it doesn't mean you're right.

Maybe listening to what people tell you is the way forward.

Anyway, here is an explanation involving pretty pictures which you might find easier to understand:

http://www.harmsy.freeuk.com/BTexp.html

[threaded]

Oliver: Good find. Post of the day!

[The Lone Gunman]

PS
All I am saying is that the same puzzle/effect or whatever you wish to call it, can be easily replicated using a geometrically perfect triangle. Without the use of any curved hypotenuse or visual tricks.

Sorry to be so argumentative, but from your own proof neither of the main triangles is geometrically perfect. The two smaller triangles have different gradients and therefore do make a straight hypotenuse. SO in one of the main triangles H is convex and in the other H is concave.

[BobTheCrate]

'tis OK LG you're not being argumentative. I think I'm the one guilty of that. Oliver and some others are gonna really love me for this now.

OK then. First your notes and then I'll move onto Oliver's supposed master piece discovery that replicates the missing square.
(it's fascinating being the only one fighting your own corner with everyone else against.)

I accept that neither triangle is geometrically perfect.

I accept in one, the hyp is everso slightly concave and the other everso slightly convex. As per Fortune Green's maths.

Now I'm asking if anyone can reconcile the missing square directly to the geometric imperfection of the triangle. Oliver's link replicates the missing square. Cruicially though it does not prove the missing square is caused by any geometric imperfection.

Because I'm stating as fact the missing square is also reproduced using sub-shapes from a geometrically perfect right angle triangle. You don't need a skew-iff hypotenuse or any other imperfection or trick to create the missing square. You just need to re-arrange the sub-shapes as you see them.

Now then, Oliver's supposed master piece discovery.

The author from that link says and I quote :-

"Most people think this is a trick, and that the shapes aren't actually the same in each image. Not so!"

(Correct. The shapes are indeed the same in each image.)

He continues ...

"The illusion lies in the fact that the red and green triangles appear to be similar. They are not. The green one is 1 square taller than the red."

Emmm ? That is no illusion. Does anyone else think that is an illusion. I don't. I think it is immediately obvious from both Oliver's link and AtW's original example that one sub triangle is one square taller than the other.

All the animated gif does is to perform the rearrangement of the sub-shapes.
The same effect would be reproduced if the hypotenuse was a geometrically straight line and the rest of the triangle including sub-triangles, are true and geometrically perfect.

[oliver]

Because I'm stating as fact the missing square is also reproduced using sub-shapes from a geometrically perfect right angle triangle.

Incredible. You still believe that to be true don't you? Even with a nice animated graphic showing you how wrong you are?

"The illusion lies in the fact that the red and green triangles appear to be similar. They are not. The green one is 1 square taller than the red."

Emmm ? That is no illusion. Does anyone else think that is an illusion. I don't. I think it is immediately obvious from both Oliver's link and AtW's original example that one sub triangle is one square taller than the other.

Hello? Anybody in there?

The actual text from the explanation is "The green one is 1 square taller than the red. To be similar, it would need to be 7·5 squares long - it's actually 8!"

It has a different gradient. Why can you not see that?

Even the explanation is over his head!

[BobTheCrate]

You're not listening again Oliver.

I've already conceeded that the two hypotenuse have everso slightly different gradients.

What I've said so many times now and I agree it's getting boring; is that the spare space is not produced by that varying gradient.

And I'm afraid your nice little graphic doesn't prove it either. All your nice little graphic does is to re-arrange the sub-shapes.

Your nice little graphic would produce exactly the same spare space using a perfectly normal right angle triangle with no kink in the hypotenuse whatsoever.

Penny dropped yet ?

[oliver]

You're not listening again Oliver.

I've already conceeded that the two hypotenuse have everso slightly different gradients.

What I've said so many times now and I agree it's getting boring; is that the spare space is not produced by that varying gradient.

Yes it is. This has been explained numerous times to you. Most of us learn how to calculate area in junior school. Were you by any chance a 'special needs' child? If so I apologise for taking things too fast for you.

And I'm afraid your nice little graphic doesn't prove it either. All your nice little graphic does is to re-arrange the sub-shapes.

No it doesn't. It shows you how the two 'overall' shapes are different and that what you assumed is a 'hypotenuse' is not straight.

Your nice little graphic would produce exactly the same spare space using a perfectly normal right angle triangle with no kink in the hypotenuse whatsoever.

Penny dropped yet ?

NO IT WOULD NOT. What will it take for you to see this? Making patently idiotic false statements over and over again doesn't make you 'right' and somehow the rest of the world 'wrong'.

How do you calculate the area of a right angled triangle?

I'll answer for you: width x height / 2

Think about that.

[BobTheCrate]

Yet again - I have already conceeded (at least 3 times now I think) that in the 2 examples, AtW's original and yours, the hypotenuse has two slightly different gradients, as per Fortune Green's calc.

I say (because I've done it) that the missing square can be produced by re-arranging the 4 sub shapes from a genuine right angle triangle.

You say NO IT WOULD NOT.

I say, 'Yes it does'. (Without hurling childish insults at you as well)

[oliver]

Yet again - I have already conceeded (at least 3 times now I think) that in the 2 examples, AtW's original and yours, the hypotenuse has two slightly different gradients, as per Fortune Green's calc.

I say (because I've done it) that the missing square can be produced by re-arranging the 4 sub shapes from a genuine right angle triangle.

You say NO IT WOULD NOT.

I say, 'Yes it does'. (Without hurling childish insults at you as well)

Congratulations - you have transcended the laws of geometry. Boy is my face red.

Oh wait. No you haven't - you're just talking out of your arse.

Why don't you print the shape off on a piece of paper and have a go?

When you have realised your mistake you can come back here and have another go.


Edited to point out that the extra 'bulge' in your experiment would not be the imaginary hypotenuse but would appear somewhere else. Unless you really did transcend the laws of geometry.

Also: bear in mind that the area of the shapes cannot change just by rearranging them.

[xoggoth]

The different slopes thing looks convincing to me. But if you can do it with both triangles having equal slope, B the C, why didnt they? It would have made it more puzzling. Or is it a red herring designed to confuse? I am going to try it your way now. If my meddling with things that man should never meddle with opens a black hole in the fabric of space and time I shall blame you.