Our objective is to define sets of numbers with dimensions. We say that a number exists in an n dimensional structure if n coordinates are required to uniquely specify it. A nice example of a 2-dimensional number system is the complex numbers. We generalise this concept by defining rotational numbers. Traditionally i is defined as the square root of -1. We use a different approach. We define rotational constants that will loop after n repeated applications.

Complex numbers are a great way of creating numbers of more than one dimension.  From Riemann’s Zeta function to the Mandelbrot set they are used to produce complex two dimensional patterns. We would like to extend this to more than two dimensions and start from first principles, like Guiseppe Peano did for natural numbers.

What follows is an informal and formal definition of rotational numbers. The same approach can be used to define even more number sets, but I will save that for a blog post.


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