Spiral Numbers
The idea is simplest when thinking in terms of polar coordinates.
For a,c > 0 and b,d real , the complex numbers satisfy
(a,b) (c,d) = (ac , b + d mod 2 pi)
The idea of spiral numbers is
(a,b)(c,d) = (ac , b + d)
So far for products.
The sum for spiral numbers is defined by
X + Y = ln( exp(X) exp(Y) ).
So it comes down to finding a good ln and exp.
My guess is exp(a,b) =
( exp(a + ab) , e b)
Where |*| is the absolute value.
And the ln is just the inverse.
For X^Y we use exp( ln X * Y ).
I wonder how the algebra works out.
Is this a good idea ?
I wonder what you think.
Regards
Tommy1729
The idea is simplest when thinking in terms of polar coordinates.
For a,c > 0 and b,d real , the complex numbers satisfy
(a,b) (c,d) = (ac , b + d mod 2 pi)
The idea of spiral numbers is
(a,b)(c,d) = (ac , b + d)
So far for products.
The sum for spiral numbers is defined by
X + Y = ln( exp(X) exp(Y) ).
So it comes down to finding a good ln and exp.
My guess is exp(a,b) =
( exp(a + ab) , e b)
Where |*| is the absolute value.
And the ln is just the inverse.
For X^Y we use exp( ln X * Y ).
I wonder how the algebra works out.
Is this a good idea ?
I wonder what you think.
Regards
Tommy1729
