What the heck...

[Boerseun]

 

I parked this in Physics and Maths, because I'm sure there must be a mathematical reason for this.

 

But:

 

If you take something with surface area x, and you cut it up into various slices, and you rearrange all the slices into some other shape, if you use all the slices, your surface area will still be x, right? Then can somebody explain the following to me?

[sanctus]

very curious. ??????

But there is something else very strange the total surface without counting the slices is :13*5/2=32.5

The sum of the surface of the slices is:

 

Dark green triangle: 5*2/2=5

Red triangle: 8*3/2=12

Green shape: =7

Orange shape: =8

Hence the total is: =32

 

Sot there seems to be a problem with total area being the sum of parts...

[Tormod]

This one has been posted before.

 

The secret lies in the angle of the longest line (compare the sizes of the triangles it leaves above the figure).

[Boerseun]

This one has been posted before. ;)

 

The secret lies in the angle of the longest line (compare the sizes of the triangles it leaves above the figure).

How's that possible?

 

The right-hand line is 5 units in length, the bottom line is 13 in length in both pics, so the line on top will be the same length and angle?

 

You don't maybe have a link to where it's been posted?

[Tormod]

Just hold a ruler against the screen and compare the straightness of the lines... ;)

[Tormod]

To be more precise, the upper line is curved.

[Tormod]

The exact same shape has been posted here, with explanations in the comments:

 

Impossible Triangle Illusion no.2 - Mighty Optical Illusions

[Boerseun]

Haha - the bastards! ;)

 

Nonetheless, printed out the curvature is vague enough for it to be a pretty cool party trick! :)

[pgrmdave]

It's easy to see that at the point five squares over and two up from the bottom left point. The hypotenuse of the bottom triangle passes through the point on the graph nearly perfectly, the top triangle is noticably lower.

[ughaibu]

This is known as Curry's paradox, though there's another paradox of the same name: Curry's Paradox (Stanford Encyclopedia of Philosophy) Here's a page including a square version: Missing square puzzle - Wikipedia, the free encyclopedia

[Eclogite]

This is a great example of why eyewitness testimony is so unreliable - about as useful as mammary devices on a masculine bovine quadruped.;)

[Qfwfq]

Just hold a ruler against the screen and compare the straightness of the lines... :)

But that's cheating! :rant:

 

 

If it's done right, the line is straight but the gridpoint is still lost in it's width, which is harder to notice! The mathematical way to look at it is by comparing the three ratios:

 

[math]\frac{2}{5}\;\frac{3}{7}\;\frac{5}{12}[/math]

 

For the intermediate point to really be on the line, they'd have to be the same.

[CraigD]

This is known as Curry's paradox, though there's another paradox of the same name: Curry's Paradox (Stanford Encyclopedia of Philosophy) Here's a page including a square version: Missing square puzzle - Wikipedia, the free encyclopedia

To clarify, the “Curry’s paradox” described in the SEoP link, and the one in the wikipedia link, have the same name only because the first name of their authors’ is omitted. The triangle and similar illusions are by armature stage magician Paul Curry, while the Liar’s paradox variation is by matematicial Haskell B. Curry.

 

Other than the last names of their authors, these 2 “paradoxes” are unrealated. The triangle is really more of an illusion, or trick, than a paradox.