This site was set up in order to give place to some radical mathematical thought, highlighted with a new infinite
series that converges to the natural logarithm.
In those pages you will find new ideas and analysis of some natural mathematical patterns.
In some of the pages I will assume that my reader possess mathematical knowledge in the related topics,
but due to the general nature of this work, the fact that it spreads across many mathematical topics,
I will attempt to explain the technique necessary to understand what it is all about. My methods are sometimes
strange to the expert mathematical eye due to the unexpected use of the mathematical objects. I urge those readers to carefully understand what I am talking about.
As my feeling is that this analysis is truly an uncharted territory, I have no doubt that the discussion is not yet complete. Your comments will be very much welcomed to my email
or at my chess club or at the thread titled "Natural Geometry - Take 2" at sci.math.
Ofer Barasofsky.
First read: On the Geometry of natural numbers - view the shapes in the shapes section or create them yourself using Galois v0.04b.
Some background philosophy (not required):
On the Philosophy of natural numbers
After reading all of that, here are my conclusions:
My personal research will continue in the attempt to prove some of the following assumptions, which might be true:
There exist a relation between S(n) and the mass of an n dimensional space point (particle). This relation is most likely to be: S(n)^2 ~ M0 or S(n) ~ M0 or S(n) ~ M0^2 where M0 is the rest mass of the particle (This assumption is based on the simple fact that the division of the circle to 4 (v=c) is the equivalency between the photon and S(4) which the first S(n) to be different then 0). So my goal is to discover the mass of all known particles as relations between S(n) where n is possibly a prime number, and also find all unknown possible particles. There is also a possibility that some possible particles are even yet to be created in the universe.
Some topological and geometrical attributes of the shapes will prove to hold the solutions to all the fundamental forces in the universe and will be vital in a grand unifying theory of gravity and the other forces.
There is a possibility that there are unit velocities to particles other then photons, that is, some particles might have a RESTING velocity or a creation velocity. This velocity for an n dimensional particle has to be in relation to f(1).
There exist a higher dimensional level of Euler's equation: e^ix=cos(x);+isin(x);, and the Galois field of higher dimensions (adding more axis to the matrix and keeping the same rules) might be able to show that.
There is a connection between the converging sum of 1/S(n) and the distribution of primes, as the shapes are depended on the division qualities of numbers and converges to an e related number, and the distribution of primes according to Gauss and Riemman is depended on the natural logarithm which is e.
