Gabriel Paul's Site
Copyright by Gabriel Paul.
Here are my ideas.
This theory is an extension of the "Complex Number Theory (CXNT)".
Though mathematicians say it is not "possible", I've created this as a way to use multidimensional numbers. Still, as mathematicians say, a basic operation in not possible, in this case: the multiplication is not distributive to adding (except for 2 general cases: with a real number, and with a real number on the second axis). Automatically "asin" and "acos" do not exist (they can not be determined because they depend on the multiplication being distributive to adding).
The whole catch is that in the MDNT there are more relational polar solutions than in the CXNT. For example, in a 2-dimensional space, each algebraic solution has 2 relational polar solutions; first: the "normal" solution; second: the module is negative and the angle is added a Pi. For a D-dimensional space there are 2 ^ (D - 1) relational polar solutions, where the module and all the angles have two choices (except the first angle which depends on all the other choices).
The fluons are, in a way, like fractals. Anyway, they were "born" because of the MDNT.
The FLT says that an object can "move" from one point to another (in a D-dimensional space) without passing through the space in between, but rather skipping all that and going like through a door.
Here are some fluons generated using multidimensional mathematical functions (in 3 dimensions):
If you would just wait for a little while, the program that generates fluons will be available on the Net. All source files (including the files with MDN functions) are included.