64=65

[Space05us]

My mom sent me an interesting e-mail today which evidently proves that 64 is equal to 65. It takes a picture of an 8x8 square cuts it into sections and then puts it all back together to create a 5x13 rectangle.

now

8x8=64
and
5x13=65

I even drew the two rectangles on paper and counted the blocks one by one labling them as I went along proving what we already know 8x8=64 and 5x13=65. Now Im pretty sure a block isnt just going to go poof and appear so I need your help to figure out what happend to it.

and if its obvious feel free to point and laugh at me all you want

[Asher]

It is an optical illusion, the segments are not all the same size in both pictures, slightly larger in the second.

[Space05us]

that still doesnt explain where an extra block came from

[Tuberski]

The extra size of the segments is equal in area to the size of one block.

ACK!

[Zylka]

Naive little world

That's an optical illusion?

[Space05us]

can you point out to me the extra block then?

[Space05us]

I mean you cant just say its an optical illusion and then say case closed I need proof darnit!

[Asher]

The problem is you're looking for an extra block, when it's not a single extra block. If it was it'd be easy to find.

Since each shape is ever-so-slightly larger, the combined effect is an effective extra block, but you can't point it out.

[Asher]

Notice the one on the right is larger...

[gopher]

Actaully, this is a well known mathematical theorm, with the answer being that the arrangement is not perfect in the second picture. A parallelogram of area 1 has been created by the cuts. Check out http://mspetkovic.tripod.com/problems.html
for it as well.

[Space05us]

thanks gopher!

asher, those picutres are from two different sections on the red piece what are you trying to prove??

[Asher]

It's the same section of the green piece, pay close attention to the hypotenuse of the green piece and notice and it does not form the exact same shape in the second picture.

[Space05us]

oh, hehe, right the green block. The red one just sticks out so much, sorry about that asher.

[:) Smiley]

Basically the slope of the hypotenuse of red and green pcs and the oblique side of the orange and blue pieces are not equal.

8/3 does not equal 5/2

[Buck Birdseed]

That's not even close to an optical illusion. There's a huge bloody gash through the second picture.