It's the most natural, geometric representation of the numbers treated as the complex objects.
In contrast to the plane of complex numbers, where a number is represented as a single point, here each number n is represented by n points (unities) distributed equally on a circle of radius n.
allows immediately to naturally decode their most important feature - DIVISIBILITY.
Every number has its own unique PATTERN OF DIVISIBILITY showing how the given number is divisible by all the other numbers smaller than itself.
Red unities are these, which are relatively prime to all the other unities belonging to numbers smaller than n.
Patterns of divisibility in a linear form:
Quantities of relatively prime unities within given number represent naturally the value of the Euler's Phi(n) function, and here, apart from the value itself, we also have its geometric representation.
What is extremely interesting and represents the natural beauty of the numbers and their mutual relations is the fact that the patterns of divisibility and thus the whole plane is "infinitely symmetrical".
The patterns on the circles represent a kind of primary symmetry in relation to the centre of the coordinate system (the whole plane is also symmetrical in relation to the X axis), but the same patterns can be found repeated infinitely many times in symmetry to the axis representing the value 1 (passing through the first relatively prime unity in a given number n).
to the axis representing value 2
to the axis representing value 3
and any other axis led through the origin and any relatively prime unity present on the numbers' plane.
What I personally love in the numbers' plane (apart from its beauty) is the fact that it gives the possibility to transfer all the possible theoretical considerations concerning numbers (even these dippest and the most sophisticated ones, concerning any of their properties, mutual relations, etc.) from the abstract sphere to the purely visual, geometric and thus very "tangible" one.
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