Thread: How many lines

last night i could'nt sleep so to changes my ideas i go on to deal whith some mathèmatical problem which lead me to the "pythagorian equation" ( integers n,m,p for wich n^2+m^2=p^2) as i could'nt solve it i went to see on wikipédia and i fall on the géometrical demonsrations of the famous pythagorus theorem(the gèomètrical one) and i was very surprise to saw so many lines on the various dèmonstrations that where proposed so i remembered one of my teacher making a very simple demonstration so i can suppose pythagorus did do the same

so here the riddle (i post this on game on puzzle section because i dont need the solution, i know it!) : how many line did pythagorus drew on the sand to demonstrate his (futur) very famous theorem to Clèopatra in order to avoid being eaten by her lions?

subsidary question : How many times shall a mountain must stand, before it is washed to the sea?

None, Pythagoras was dead long before Cleopatra was born.

Pyhthagoras died around 580 BC and Cleopatra was born in 69 BC.

this historical objection is irrelevant
we are nor speaking of the same clèopatra!
and we are in a section were can be told very incredible stories!

i' ve been peeping at the resolution of this geometrical problem in wikipèdia
there's only (by the day i took a look) one solution left but it seems to me it's deriberatly complicate (might it be true ?)

i think that wath's is the most interesting in math is that you can find à multitudes of ways to solve the same problem

so the simplest solution that i would like a few of you spend five to twenty minuts on it takes only M lines! thats not much and you'll agreed with me to say it's probaly the minimum!

we have the relation 2* square-root-off(M)=M

no much figure to draw it seems!

please don't post the solution to qweekly (but you can confirm i'm not telling you craps!)