Thread: from i to π View Single Post
2016-09-07, 17:54   #21
science_man_88

"Forget I exist"
Jul 2009
Dartmouth NS

2×3×23×61 Posts

Quote:
 Originally Posted by bhelmes A peaceful day for all, i count the amount of number with c=u²+v² with gcd (u, v)=1 and c < 2^n or better all the combination with u²+v²<2^n and gcd (u,v)=1 i do not understand what the gcd (u, v)=1 makes with the result. the gcd (u,v)=1 is important for the construction of primitiv pyth. triples as far as i can see. for example: limit = 2^5 = 32 u, v = 1, 2 = 2, 3 = 2, 5 = 3, 4 Besides for me is the pair (2,5)=(5,2) For every combination of (u,v) i could construct a=u²-v², b=2uv and c=u²+v² m=a/c and n=b/c is a vector in the unit circle But i did not get the relationship with 2pi Any ideas ? Greetings from the primes Bernhard
http://www.tsm-resources.com/alists/trip.html

you could generate it with two variables m and n. m>n. then the gcd is only important because if two sides have a gcd>1 then the sum that gets rooted will have that factor if it has it an even number of times ( power wise) then the square root will have it as well. or that's my main understanding of it though if all three have a GCD>1 it allows that to be divided out and the pythagorean theorem will work out for the lower version. edit: doh forgot all primitive ones have and even and an odd leg so a gcd greater than 1 means it can't be primitive.

Last fiddled with by science_man_88 on 2016-09-07 at 18:02