64=65

Space05us · October 20, 2003, 20:33

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 · October 20, 2003, 20:35

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

Space05us · October 20, 2003, 20:36

that still doesnt explain where an extra block came from

Tuberski · October 20, 2003, 20:38

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

ACK!

Zylka · October 20, 2003, 20:40

That's an optical illusion?

Space05us · October 20, 2003, 20:42

can you point out to me the extra block then?

Space05us · October 20, 2003, 20:43

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

Asher · October 20, 2003, 20:44

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 · October 20, 2003, 20:47

Notice the one on the right is larger...

gopher · October 20, 2003, 20:49

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 · October 20, 2003, 20:57

thanks gopher!

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

Asher · October 20, 2003, 21:01

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 · October 20, 2003, 21:04

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

:) Smiley · October 25, 2003, 02:21

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 · October 25, 2003, 05:14

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

Urban Ranger · October 25, 2003, 07:13

But you can do it with carpets if you accidentally burnt a hole in the middle of it.

Harovan · October 25, 2003, 07:39

This one's pretty old. :) Smiley has it right, the slopes aren't exacty the same. Basically the "diagonal" of the 5x13 is not a line but a very slim parallelogram with the area of one tile.

JohnT · October 25, 2003, 10:00

Quote:

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

It's an optical illusion if you have my crappy eyesight.

Kuciwalker · October 25, 2003, 10:09

This is in DOZENS of puzzle books.

Space05us · October 25, 2003, 11:25

Quote:

This one's pretty old.

Smiley has it right, the slopes aren't exacty the same. Basically the "diagonal" of the 5x13 is not a line but a very slim parallelogram with the area of one tile.

yeah, he probably read gophers post but then was so amazed by the illusion that he had to give the answer, and you in turn did the same.