Author Topic: a^2 + b^2 = c^2  (Read 6175 times)

0 Members and 1 Guest are viewing this topic.

Offline Genesis

  • Elevator Action Operator
  • *****
  • Posts: 2593
  • Greetings.
    • View Profile
a^2 + b^2 = c^2
« on: June 20, 2006, 10:15:27 pm »
Prove or disprove that, if n be a number greater than 2, there are no whole numbers such that a^n +b^n =c^n

a, b, and c have to be positive and n > 2

Enjoy! I don't think even Oviraptor can solve this one!

PM me if you think you have it, and feel free to post comments and hints here.
« Last Edit: June 20, 2006, 11:34:47 pm by Genesis »



What will you do?

Offline Kratok

  • Turkey Shoot Terminator
  • *****
  • Posts: 3179
  • Probably dead at this point!
    • View Profile
    • [url=http://la-mulana.com/en/][img]http://la-mulana.com/banner/half_banner3.gif[/img][/url]
Re: a2 + b2 = c2
« Reply #1 on: June 20, 2006, 10:18:10 pm »
I
B
A
Y

Offline Clayface

  • Jungle Hunter
  • *****
  • Posts: 1653
  • user #9
    • View Profile
Re: a2 + b2 = c2
« Reply #2 on: June 20, 2006, 11:13:07 pm »
a2 + b2 = c2


 ???
do you mean a^2+b^2=c^2
or 2a + 2b = 2c
im confused

Offline Genesis

  • Elevator Action Operator
  • *****
  • Posts: 2593
  • Greetings.
    • View Profile
Re: a2 + b2 = c2
« Reply #3 on: June 20, 2006, 11:13:42 pm »
The first one.

What will you do?

Offline Clayface

  • Jungle Hunter
  • *****
  • Posts: 1653
  • user #9
    • View Profile
Re: a2 + b2 = c2
« Reply #4 on: June 20, 2006, 11:14:29 pm »
and do you want us to write it out as a proof?


Offline Genesis

  • Elevator Action Operator
  • *****
  • Posts: 2593
  • Greetings.
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #5 on: June 20, 2006, 11:15:41 pm »
Explaining your conclusion is the entire point.

What will you do?

Offline Clayface

  • Jungle Hunter
  • *****
  • Posts: 1653
  • user #9
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #6 on: June 20, 2006, 11:20:50 pm »
well that only works with multiples of 3,4,and 5 plugged into a,b,and c respectably,

so
3^2+4^2=5^2
6^2+8^2=10^2
. . . .
. . . .
45^2+60^2=75^2
ect,

if you try plugging in any numbers that dont follow that pattern, it wont work.

Offline Daxx

  • Golden Axe Battler
  • *****
  • Posts: 8613
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #7 on: June 20, 2006, 11:23:12 pm »
Let a=c and b=0 (alternatively, let a=0 and b=c).

The equation now holds for all non-zero values of n.
« Last Edit: June 20, 2006, 11:31:29 pm by Daxx »

Offline Genesis

  • Elevator Action Operator
  • *****
  • Posts: 2593
  • Greetings.
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #8 on: June 20, 2006, 11:33:49 pm »
Sorry, forgot to put that a, b, and c have to be positive and n > 2 I'll add that now. Sorry I forgot that but its 2:30 for me right now.

What will you do?

Offline Clayface

  • Jungle Hunter
  • *****
  • Posts: 1653
  • user #9
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #9 on: June 20, 2006, 11:42:29 pm »
that would be very very easy to prove wrong.

Offline Genesis

  • Elevator Action Operator
  • *****
  • Posts: 2593
  • Greetings.
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #10 on: June 20, 2006, 11:43:22 pm »
Do it.

What will you do?

Offline Quantum Burrito

  • K.C. Munchkin Maestro
  • ****
  • Posts: 948
  • Up, Down, Strange, Charm, Top, Bottom, Burrito
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #11 on: June 20, 2006, 11:44:31 pm »
that would be very very easy to prove wrong.

*uncontrolable laughter*

*snort* where do they come from?
Quote from: The Will
In a movie, one can always pull back and condemn the character or the artist ... But in playing a game ... we can be encouraged to examine our own values by seeing how we behave within virtual space.
tl;dr. But with all those shiny symbols and numbers it's probably awsome.

Offline Genesis

  • Elevator Action Operator
  • *****
  • Posts: 2593
  • Greetings.
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #12 on: June 20, 2006, 11:46:33 pm »
Wait do you mean what I forgot to add, **** I KNEW that would happen! WHY does nobody believe me when I forget something?  :'(

What will you do?

Offline Clayface

  • Jungle Hunter
  • *****
  • Posts: 1653
  • user #9
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #13 on: June 20, 2006, 11:51:52 pm »
well one way to prove it wrong would be to sell the values of a, b, and c all to 3

3^2+3^2=3^2
9+9=9
18=9

. . . .
WRONG

Offline Daxx

  • Golden Axe Battler
  • *****
  • Posts: 8613
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #14 on: June 20, 2006, 11:53:39 pm »
well one way to prove it wrong would be to sell the values of a, b, and c all to 3

3^2+3^2=3^2
9+9=9
18=9

. . . .
WRONG

Uh, no. That's not a proof that there are no numbers which satisfy the equation. It's like saying that there are no numbers which satisfy x+1=2 by using x=3 as a demonstration.

Offline Quantum Burrito

  • K.C. Munchkin Maestro
  • ****
  • Posts: 948
  • Up, Down, Strange, Charm, Top, Bottom, Burrito
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #15 on: June 20, 2006, 11:56:14 pm »
a, b, and c have to be positive and n > 2

Quote from: The Will
In a movie, one can always pull back and condemn the character or the artist ... But in playing a game ... we can be encouraged to examine our own values by seeing how we behave within virtual space.
tl;dr. But with all those shiny symbols and numbers it's probably awsome.

Offline Clayface

  • Jungle Hunter
  • *****
  • Posts: 1653
  • user #9
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #16 on: June 21, 2006, 12:00:57 am »
well that only works with multiples of 3,4,and 5 plugged into a,b,and c respectably,

so
3^2+4^2=5^2
6^2+8^2=10^2
. . . .
. . . .
45^2+60^2=75^2
ect,

if you try plugging in any numbers that dont follow that pattern, it wont work.

those are all the numbers that satisfy the equation, as I stated before, I just posted an example of how the equation doesnt work with all numbers.

and @ quantum Burrito, how did I not read right?
all the numbers I used follow'd the outline.


sorry for bad termanology / spelling

Offline Genesis

  • Elevator Action Operator
  • *****
  • Posts: 2593
  • Greetings.
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #17 on: June 21, 2006, 12:05:40 am »
n > 2

What will you do?

Offline Clayface

  • Jungle Hunter
  • *****
  • Posts: 1653
  • user #9
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #18 on: June 21, 2006, 12:17:32 am »
it is > 2

Offline Genesis

  • Elevator Action Operator
  • *****
  • Posts: 2593
  • Greetings.
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #19 on: June 21, 2006, 12:19:49 am »
OK, I've officialy lost you, what problem are you doing exactly?

What will you do?

Offline Daxx

  • Golden Axe Battler
  • *****
  • Posts: 8613
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #20 on: June 21, 2006, 12:21:46 am »
it is > 2

Dear god, and you claim to be two years advanced in maths?

Offline Clayface

  • Jungle Hunter
  • *****
  • Posts: 1653
  • user #9
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #21 on: June 21, 2006, 12:24:49 am »
gahhhh

screw off, all of you,

I cant think straight.
 :-[ :-X :-[

havn't been in school in like a month.

Offline Oviraptor

  • Moderator
  • R-Type Force Pod
  • *****
  • Posts: 6684
  • tastes just like chicken
    • View Profile
    • Oviraptor's World
Re: a^2 + b^2 = c^2
« Reply #22 on: June 22, 2006, 12:29:55 pm »
Fermat's last theorum, eh?

http://math.stanford.edu/~lekheng/flt/wiles.pdf

What he said.

Offline stuck

  • Robotron Automaton
  • *****
  • Posts: 1877
  • Who is John Galt?
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #23 on: June 22, 2006, 02:40:18 pm »
arrgh.. Oviraptor beat me to it. >:(
Yea, what he said.

I think there was a 200 page proof for this.

Offline Aybraus

  • Mr. Do! Disciple
  • *****
  • Posts: 2177
  • aka VFX Watch aka Toothy aka Chris.
    • View Profile
What now!
« Reply #24 on: June 22, 2006, 05:43:42 pm »
I challenge you to prove that, only knowing that r2π=Acircle, prove that dπ=C

π being pi incase you can't load up unicode.
I'm toothy22 on Steam. Someone needs to invite me into the GS clan!

Offline Genesis

  • Elevator Action Operator
  • *****
  • Posts: 2593
  • Greetings.
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #25 on: June 23, 2006, 11:26:21 am »
Y'know, I just KNEW that Oviraptor would be the one to ruin my fun with this.   :D
Don't worry, I'm not mad, I might have been if you didn't know better though....

Good job!

What will you do?

Offline stuck

  • Robotron Automaton
  • *****
  • Posts: 1877
  • Who is John Galt?
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #26 on: June 23, 2006, 03:52:24 pm »
Ok, I'll have a crack at it.

On second thought, you need to also know some axioms such as the relationship between a regular polygons area and perimeter.

So that is: kl2 = k2l

k is a constant depending on the number of sides, and l is a side length.

We see that Kl2 = (pi)r2 in this case.

Therefore, we set K = pi and l = r; If you want to make l = diameter, then k = (pi)/2

Substitute this in for the other equation (transitive property, I think. Three years since geometry and proofs) and you get 2(pi)r = C.


I think I just made up some rules, but feel free to approve of this. Then again, you may need some calculus to really prove it. Calculus which I don't have.

EDIT: This basic rule should work (the axiom that I outlined) with regular polygons. It works with rectangles (k = 1), triangles, though, is on shaky footing. But I know there is a formal relation somewhere.

EDITEDIT: triangles k is sqr(3)/4
« Last Edit: June 24, 2006, 07:21:18 pm by stuckin2004 »

Offline Aybraus

  • Mr. Do! Disciple
  • *****
  • Posts: 2177
  • aka VFX Watch aka Toothy aka Chris.
    • View Profile
Re: a^2 + b^2 = c^2
« Reply #27 on: June 25, 2006, 04:16:19 pm »
My chalange still stands.
I'm toothy22 on Steam. Someone needs to invite me into the GS clan!