Have I Gone Mad? [Will You?]

[Rh0ads]

Hhhmmm,

A friend sent me a link to an optical illusion page. I scrolled quickly through it, finding nothing too special. But, then I found the image below.



Can anyone make sense of it and why there is that hole?

Thanks
-George

[NoteMe]

I have looked at that one before..it made me mad too..I wanted to print them out, and cut it out, and try to see if they realy where the same size...

[Merrion]

The slope on the two triangles is not the same (2:5 vs 3:8)....

[mendhak]

That hole? Check to make sure you didn't divide by zero somewhere...

[NoteMe]

Originally posted by Merrion
The slope on the two triangles is not the same (2:5 vs 3:8)....

??? What do you mean...the BIG one? it is X=13, Y=5...

[NoteMe]

ohhh...maybe I see what you mean...the one at the bottom is maybe 1,2mm higher on the hypotenus, then the one at the top...

[alkatran]

I used paint to move them around and got the same results. I'm thinking that there's a small differenrnce between the triangles that we don't notice. Basic geometry tells us that this is ridiculous.

[NoteMe]

Look at the hypotenus...look at the grid right over the two triangles...doesn't it look like the one at the bottom is about 1,2mm "taller", if so, would that be enough for a 1cm^2 square?

[alkatran]

Alright I got something:

Triangle = 5 x 13.
Area = 5*13/2 = 32.5

First triangle parts:
Green = 8
Orange = 7
Red = 8x3
Dark green = 5x2
Total area = 8+7+8*3/2+5*2/2
=8+7+4*2+5
=15 + 12 + 5
= 32

Second triangle parts = first triangle parts + 1 = 33

Triangle = 32.5
Triangle parts (1) = 32
Triangle parts (2) = 33

HMMMMmmmm

[NoteMe]

But can't anyone else then me see that the hypotenus on the second picture is a bit "taller" then on the first one....if so...it is actualy one square bigger, it is just devided on the whole hypotenus...

[alkatran]

The hypotenus of the triangle is sqr(5^2+13^2) = 13.928

Looks like you wouldn't need ot add much length on either side for an extra 1.

[NoteMe]

I know..and it looks like it is a mm taller or something like that...so I think that is the solution..

[PT Exorcist]

The squares bellow are smaller than above - bah that was an easy one

[alkatran]

13*5/2 = 32.5

(13+x)*(5+x)/2 = 33
.5x^2 + 9x + 32.5 = 33
.5x^2 + 9x -.5 = 0
x = (-9 +- sqr(9^2 - 4*.5*-.5))/.5*2
=(-9 +- sqr(81 + 1)/2
=(-9 +- 9.05538)/2
=-4.5 +- 4.5267
=.0267

(13+x)*(5+x)/2 = 32
.5x^2 + 9x + 32.5 = 32
.5x^2 + 9x + .5 = 0
x = (-9 +- sqr(9^2 - 4*.5*.5))/.5*2
=(-9 +- sqr(81 - 1)/2
=(-9 +- 8.944)/2
=-4.5 +- 4.472
=-.0278

.0267 - - .0278 = .0545

It takes a 20th of a square to change it by 1. Judging purely by sight, that's like 3 millimeters on that graph.

Well, doesn't take much, does it?

[wossname]

This is so obvious.

The orange and light green blocks are the important ones. The triangles can be discarded.

In the top picture the 2 blocks fit snugly to form a rectangle. But they only fit snugly in this configuration, if you try to fit them any other way you don't get a rectangle.

There is absolutely no mystery here whatsoever, its not even an illusion.

However, it is very gay and I am frankly ashamed of you 'learned' coders that should know better than to start thinking like a lowly user (spit).

You are all to write out 1000 lines: "I must not think like a user."

NO writing a script to do it for you and NO copy/pasting! Naughty!

[alkatran]

Excuse me, but the triangles are part of the illusion as well. The ENTIRE triangle needs to be SLIGHTLY bigger (I figured 3mm) to add that extra square. Otherwise fitting them in a non-perfect rectangle wouldn't work, would it?

I'd also like to point out that I did examine each piece individually. I especially looked at how those two squarish pieces fit together (since the space was directly related to them).

[alkatran]

I like how the problem says the "partitions" are "exactly" the same as above.

BTW: I just reliazed that the increase in size could be entirely hidden within that thick black line dividing the peices. The only reason it's so thick is to hide the illusion.

[NoteMe]

Originally posted by alkatran

BTW: I just reliazed that the increase in size could be entirely hidden within that thick black line dividing the peices. The only reason it's so thick is to hide the illusion.

Yeah it is. If it is on the inside on one of them and on the outside on the other one, it should be more then enough. I guessed it was just part of it. But now I start to think it is the whole ilution..

[NoteMe]

Actualy after looking at it again, it looks more like if you look at the black line on the hypotenus is at the same place on both pictures in the start and in the end, but that it goes from the inner edge to the outer edge in the middle on the picture on the bottom. Can that be true? I don't have any drawing apps on this computer to test it with...

[TheVader]

Placing them on top of each other clearly shows the difference...

[wossname]

Now children, lets do some maths.

[NoteMe]

Originally posted by TheVader
Placing them on top of each other clearly shows the difference...

So I was 100% right about the line being "higher" in the midle of the hypotenus......I AM SOOOO GOOOOD...

[Shaggy Hiker]

The illusion then is that the two collections of shapes form triangles. In fact, neirther collection is actually a triangle, but is an unusual four sided polygon. Just by noticing that the slopes of the hypotenuses of the two component triangles are different, it stands that the collection shape cannot be a three sided figure.

[Electroman]

Posted by wossname
Now children, lets do some maths.

[Electroman]

Posted by NoteMe
So I was 100% right about the line being "higher" in the midle of the hypotenus......I AM SOOOO GOOOOD...

Apart from Merrion said it first and he made more sense

[NoteMe]

Originally posted by Electroman
Apart from Merrion said it first and he made more sense

I didn't understand what he said...made no sense for me, and 2:5 and so on we use here in Norway for map mesures, and size of objects, not talking about a hypotenus that actualy is a besier patch or what the **** it is called in English..

[NoteMe]

Bezier Curve maybe???

[Electroman]

Posted by NoteMe
I didn't understand what he said...made no sense for me, and 2:5 and so on we use here in Norway for map mesures, and size of objects, not talking about a hypotenus that actualy is a besier patch or what the **** it is called in English..

Red triangle is 5 by 3 and the green is 2 by 5. As factors these aren't equal so he was saying the gradient on the two triangles isn't the same .

[NoteMe]

So why didn't he say that in the beginning..

[Electroman]

Posted by NoteMe
So why didn't he say that in the beginning..

Haha

[alkatran]

Oh, I get it. With the red on the bottom it means that there is a dent created, and on the top a point is created.

So it really is the same parts.

[NoteMe]

Can't people start to write English?


DENT: (from dictionary.com)

dent2 ( P ) Pronunciation Key (dnt)
n.

See tooth.

No way it is creating a tooth...

[alkatran]

A dent is usually something going inward (if you chuck a rock at a car, it will make a dent in it).

I like how it said "see tooth" because dent is how you spell tooth in french.

[mendhak]

Originally posted by alkatran
(if you chuck a rock at a car, it will make a dent in it).

No, if you chuck a rock at a car, you will lose a "dent".

[BodwadUK]

I only see a red cross no illusion there

[NoteMe]

Originally posted by alkatran
A dent is usually something going inward (if you chuck a rock at a car, it will make a dent in it).

I like how it said "see tooth" because dent is how you spell tooth in french.

Dentist...