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OffTopic > Fermat's last theorum: how do you think he did it

#129808 - keldon - Sun May 27, 2007 3:39 pm

http://en.wikipedia.org/wiki/Fermat's_last_theorem

How do you think Fermat could have concluded his proof for x^n + y^n = z^n has no integer solutions for n>2? The proof we have uses maths that did not exist back then. I have my suspicions at it being something to do with the following:

1: (a+1)^n - a^n is greater than a^n - (a-1)^n for any a > 0
2: a^(n+1) > a^n for any a > 1 and n > 0
3: if (a+1)^n - a^n > (a^n)*2 for any a > 1 then there is no b such that a^n + b^n >= c^n where b < c and a < c
4: there is no solution where x=1 or y=1 for any n>1
5: there is no x where x^n = y^n and x!=y for any n>0
6: for all n>2 (a+1)^n - a^n > (a^n)*2 when a=2, therefore there is no solution for any n>2

#129842 - Dood77 - Mon May 28, 2007 1:56 am

Never heard of this yet... but I've always wondered how the heck Avogadro came up with his magical number.
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#129851 - keldon - Mon May 28, 2007 8:50 am

http://www.bulldog.u-net.com/avogadro/avoga.html

Seems to be good old fashion experimentation; pretty neat since they were all exploring new ground.

#129885 - Tikker - Mon May 28, 2007 5:44 pm

I'd have loved to have been there when they were trying to convince people of pi


".....Ok, so it's a number that we can't exactly define, but it works! don't ask us how or why, it just does! oh yeah, let's also just represent it with this symbol since we can't really figure out that the exact value is"

#129899 - spinal_cord - Mon May 28, 2007 10:30 pm

Code:
                              ___
                            _//_\\
                          ,"    //".
   Mmmmmmmmm...          /          \
      Pi...            _/           |
                      (.-,--.       |
                      /o/  o \     /
                      \_\    /  /\/\
                      (__`--'   ._)
                      /  `-.     |
                     (     ,`-.  |
                      `-,--\_  ) |-.
                       _`.__.'  ,-' \
                      |\ )  _.-'    |
                      i-\.'\     ,--+.
                    .' .'   \,-'/     \


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#129900 - keldon - Mon May 28, 2007 10:31 pm

lol; well it is interesting how different mathematicians approach its calculation.