21-10-2003 05:33									#1
	64=65 Support Apolyton buy from Amazon

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

Attachment: 64x65.jpg
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	21-10-2003 05:35									#2
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It is an optical illusion, the segments are not all the same size in both pictures, slightly larger in the second.

	21-10-2003 05:36									#3
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that still doesnt explain where an extra block came from

	21-10-2003 05:38									#4
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The extra size of the segments is equal in area to the size of one block.

ACK!

	21-10-2003 05:40									#5
	Naive little world Support Apolyton, pre-order Civilization IV

That's an optical illusion?

	21-10-2003 05:42									#6
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can you point out to me the extra block then?

	21-10-2003 05:43									#7
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I mean you cant just say its an optical illusion and then say case closed I need proof darnit!

	21-10-2003 05:44									#8
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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.

	21-10-2003 05:47									#9
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Notice the one on the right is larger...

Attachment: hah.jpg
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	21-10-2003 05:49									#10
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

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.

	21-10-2003 05:57									#11
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thanks gopher!

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

	21-10-2003 06:01									#12
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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.

	21-10-2003 06:04									#13
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oh, hehe, right the green block. The red one just sticks out so much, sorry about that asher.

	25-10-2003 11:21									#14
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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

	25-10-2003 14:14									#15
	Increase the size of your Attachments

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

	25-10-2003 16:13									#16
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But you can do it with carpets if you accidentally burnt a hole in the middle of it.

	25-10-2003 16:39									#17
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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.

	25-10-2003 19:00									#18
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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.

	25-10-2003 19:09									#19
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This is in DOZENS of puzzle books.

	25-10-2003 20:25									#20
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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.

	25-10-2003 20:37									#21
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That's a pretty good one. Never seen this, before.

	26-10-2003 00:04									#22
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Pythagorus save us!

	26-10-2003 00:43									#23
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AHH! AHH! AHH!

NO MORE MATH!!!

	26-10-2003 02:39									#24
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Its not math- its geometry.

	26-10-2003 02:51									#25
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It's all the same for humanities majors.