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Spiral Numbers
#1
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
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Messages In This Thread
Spiral Numbers - by tommy1729 - 11/19/2015, 10:20 PM
RE: Spiral Numbers - by tommy1729 - 11/20/2015, 01:13 PM
RE: Spiral Numbers - by tommy1729 - 02/29/2016, 10:56 PM
RE: Spiral Numbers - by tommy1729 - 02/29/2016, 11:12 PM
RE: Spiral Numbers - by marraco - 03/01/2016, 12:38 AM
RE: Spiral Numbers - by Gottfried - 03/01/2016, 12:30 PM
RE: Spiral Numbers - by tommy1729 - 03/01/2016, 01:27 PM
RE: Spiral Numbers - by Gottfried - 03/01/2016, 04:16 PM
RE: Spiral Numbers - by tommy1729 - 03/01/2016, 09:53 PM
RE: Spiral Numbers - by tommy1729 - 03/01/2016, 10:15 PM

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