So you think you're smart? Here's your chance to show off. Whomever can CORRECTLY explain why and how this is so...well, I will give myself a tempban.
Ready?
Go.
Ready?
Go.
x = y
u can apply temp ban now?
u can apply temp ban now?
Sort of explains this sum.
Baked my head - Good sum to try to work out.
Unexplainable from the eyes of a GCSE student.
2di5coz
Cant be arsed unless its a week or more. Its probably over my level to.
It's crazy to actually expect you to have to THINK for once, I know.kptk92 wrote:
x = y
u can apply temp ban now?
Now stop spamming my thread, lest you want an AWM.
thats wild
The 64 = 65 paradox arises from the fact that the edges of the four pieces, which lie along the diagonal of the formed rectangle, do not coincide exactly in direction. This diagonal is not a straight segment line but a small lozenge (diamond-shaped figure), whose acute angle is
arctan 2/3 - arctan 3/8 = arctan 1/46
which is less than 1 degree 15' . Only a very precise drawing can enable us to distinguish such a small angle. Using analytic geometry or trigonometry, we can easily prove that the area of the "hidden" lozenge is equal to that of a small square of the chessboard.
Goodbye
EDIT:we did this back in high school it's so basic o.O
pictures ahere http://mathworld.wolfram.com/DissectionFallacy.html
arctan 2/3 - arctan 3/8 = arctan 1/46
which is less than 1 degree 15' . Only a very precise drawing can enable us to distinguish such a small angle. Using analytic geometry or trigonometry, we can easily prove that the area of the "hidden" lozenge is equal to that of a small square of the chessboard.
Goodbye
EDIT:we did this back in high school it's so basic o.O
pictures ahere http://mathworld.wolfram.com/DissectionFallacy.html
Last edited by Aries_37 (2008-03-19 16:59:49)
Well gimme a clue then, sorry if I'm not very pr0 at Maths but when theres a mod temp'ing himself, I'm very tempted to do anything necessary.ThomasMorgan wrote:
It's crazy to actually expect you to have to THINK for once, I know.kptk92 wrote:
x = y
u can apply temp ban now?
Now stop spamming my thread, lest you want an AWM.
The repositioning of the orange pieces requires the grey pieces to be repositioned in order to form a perfect rectangle. Because the arrangement has been shifted, the figures take up more space on the plane, as their new interlocked positions dictate so. Each individual figure does not increase in size, but a simple re-arrangement changes the size of the mass as a whole
Drawn wrong. If you assume the black lines go through the intersections on the second one and add up the areas of the individual shapes, you get 64. Pretty sure.
Edit: Aries beat me to it. The picture when drawn looks to be exactly hitting the same places, but it isn't, it's off. The extra 1 area is distributed throughout the length of the edge that really doesn't meet.
Edit: Aries beat me to it. The picture when drawn looks to be exactly hitting the same places, but it isn't, it's off. The extra 1 area is distributed throughout the length of the edge that really doesn't meet.
brainden.com/forum/index.php?showtopic=139Aries_37 wrote:
The 64 = 65 paradox arises from the fact that the edges of the four pieces, which lie along the diagonal of the formed rectangle, do not coincide exactly in direction. This diagonal is not a straight segment line but a small lozenge (diamond-shaped figure), whose acute angle is
arctan 2/3 - arctan 3/8 = arctan 1/46
which is less than 1 degree 15' . Only a very precise drawing can enable us to distinguish such a small angle. Using analytic geometry or trigonometry, we can easily prove that the area of the "hidden" lozenge is equal to that of a small square of the chessboard.
Goodbye
EDIT:we did this back in high school it's so basic o.O
pictures ahere http://mathworld.wolfram.com/DissectionFallacy.html
Plagerism
Reverse process
You get banned.
Edit:
That page seems to be down, but heres the proof
Last edited by Mitch (2008-03-19 17:02:11)
15 more years! 15 more years!
Winner.Aries_37 wrote:
The 64 = 65 paradox arises from the fact that the edges of the four pieces, which lie along the diagonal of the formed rectangle, do not coincide exactly in direction. This diagonal is not a straight segment line but a small lozenge (diamond-shaped figure), whose acute angle is
arctan 2/3 - arctan 3/8 = arctan 1/46
which is less than 1 degree 15' . Only a very precise drawing can enable us to distinguish such a small angle. Using analytic geometry or trigonometry, we can easily prove that the area of the "hidden" lozenge is equal to that of a small square of the chessboard.
Goodbye
EDIT:we did this back in high school it's so basic o.O
pictures ahere http://mathworld.wolfram.com/DissectionFallacy.html
See you guys in three.
However, in doing so, you've plagiarized. Enjoy your three day vacation with me.
hehe...I did that in grade 8. Nice work Aries_37
I knew the answer to that question all along
/party
/party
lol e-detectiveMitch wrote:
brainden.com/forum/index.php?showtopic=139Aries_37 wrote:
The 64 = 65 paradox arises from the fact that the edges of the four pieces, which lie along the diagonal of the formed rectangle, do not coincide exactly in direction. This diagonal is not a straight segment line but a small lozenge (diamond-shaped figure), whose acute angle is
arctan 2/3 - arctan 3/8 = arctan 1/46
which is less than 1 degree 15' . Only a very precise drawing can enable us to distinguish such a small angle. Using analytic geometry or trigonometry, we can easily prove that the area of the "hidden" lozenge is equal to that of a small square of the chessboard.
Goodbye
EDIT:we did this back in high school it's so basic o.O
pictures ahere http://mathworld.wolfram.com/DissectionFallacy.html
Plagerism
Reverse process
You get banned.
Its the way that you re-arrange the shapes. The Triangles and Trapazoids all have the same area no matter what, however if you arrange their combined areas in a different pattern it could come out slightly more. In the 8x8 image they are more close to eachother, more compact. The in 5x13 one they are more spread out which allows them to take up more (but not much more) combined space.
very very very easy, the sum of the triangles becomes a greatter distance if placed to make a rectangle at the ends thus filling in the rest with the other shapes.. easy now ban ya self
lol nice oneDoctaStrangelove wrote:
Its the way that you re-arrange the shapes. The Triangles and Trapazoids all have the same area no matter what, however if you arrange their combined areas in a different pattern it could come out slightly more. In the 8x8 image they are more close to eachother, more compact. The in 5x13 one they are more spread out which allows them to take up more (but not much more) combined space.
pr0 tbhThomasMorgan wrote:
However, in doing so, you've plagiarized. Enjoy your three day vacation with me.
Last edited by Aries_37 (2008-03-19 17:05:31)
Motherfuckin ownedThomasMorgan wrote:
Winner.Aries_37 wrote:
The 64 = 65 paradox arises from the fact that the edges of the four pieces, which lie along the diagonal of the formed rectangle, do not coincide exactly in direction. This diagonal is not a straight segment line but a small lozenge (diamond-shaped figure), whose acute angle is
arctan 2/3 - arctan 3/8 = arctan 1/46
which is less than 1 degree 15' . Only a very precise drawing can enable us to distinguish such a small angle. Using analytic geometry or trigonometry, we can easily prove that the area of the "hidden" lozenge is equal to that of a small square of the chessboard.
Goodbye
EDIT:we did this back in high school it's so basic o.O
pictures ahere http://mathworld.wolfram.com/DissectionFallacy.html
See you guys in three.
However, in doing so, you've plagiarized. Enjoy your three day vacation with me.
15 more years! 15 more years!
There is actually a small gap between the hypotenuses of the horizontal right triangles.
Cake for everyone
Definition of butt-fucked: Tmo and his Magical Mathematics Questions.Mitch wrote:
Motherfuckin ownedThomasMorgan wrote:
Winner.Aries_37 wrote:
The 64 = 65 paradox arises from the fact that the edges of the four pieces, which lie along the diagonal of the formed rectangle, do not coincide exactly in direction. This diagonal is not a straight segment line but a small lozenge (diamond-shaped figure), whose acute angle is
arctan 2/3 - arctan 3/8 = arctan 1/46
which is less than 1 degree 15' . Only a very precise drawing can enable us to distinguish such a small angle. Using analytic geometry or trigonometry, we can easily prove that the area of the "hidden" lozenge is equal to that of a small square of the chessboard.
Goodbye
EDIT:we did this back in high school it's so basic o.O
pictures ahere http://mathworld.wolfram.com/DissectionFallacy.html
See you guys in three.
However, in doing so, you've plagiarized. Enjoy your three day vacation with me.
Good Job on the Plagiurism. (Spelling*)
So, are there any bans flying tonight?
The idea of any hi-fi system is to reproduce the source material as faithfully as possible, and to deliberately add distortion to everything you hear (due to amplifier deficiencies) because it sounds 'nice' is simply not high fidelity. If that is what you want to hear then there is no problem with that, but by adding so much additional material (by way of harmonics and intermodulation) you have a tailored sound system, not a hi-fi. - Rod Elliot, ESP
Omg!!! Caek!
