Thread: from i to π
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Old 2016-09-07, 17:54   #21
science_man_88's Avatar
"Forget I exist"
Jul 2009
Dartmouth NS

2×3×23×61 Posts

Originally Posted by bhelmes View Post
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

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

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
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