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#1 Re: Exercises » Euclidean geometry problems » 2012-10-07 21:29:09

Oops..x>1 in line three please...typo!

#2 Re: Exercises » Euclidean geometry problems » 2012-10-07 21:27:09

Can we assume that if x>1 that ln(x) >x -1 (??)
therefore                                   x > exp(x - 1) = exp(x) / e
x .1 means  for all x there must exist p>0  such that x=1+p and substituting this for x we see that
                                          1 + p > exp(1+p)/e = exp(p).e/e = exp(p)
Our assumption produces then  1+p > exp(p) and this is false if p=2,3,4,.......
So assumption is false, proving the result.

#3 Re: Puzzles and Games » Can you suggest six names of great mathematicians quickly? » 2012-10-07 20:10:14

Thales, Archimedes, Eudoxus, Euclid, Diophantus, Newton are six pretty prominent guys.

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