horn torus model step by step

the horn torus is an associative aid to illustrate complex numbers.

the horn torus has two possibilities (degrees of freedom) for

1. rotation as spin around the main symmetry axis (two directions)

2. revolution of longitudes,

kind of rolling along the main symmetry axis with

- the axis (= horns of infinitely big tori) can be associated with time.

combine both turns with particular ratios to get different trajectories

respectively for the increasing horn torus a complex 'unrolling line'

as fundamental entity containing all possible resonances (

the rate of rotation symbolises the real part of a complex number,

the unrolled distance from size zero symbolises the imaginary part

and every section of the entity is assigned to one complex number

i.e. complex numbers represent all different particles in

where 'particles' don't populate any construction like vector spaces

but form their own space as aggregate of all infinitely many entities

which are represented in

recap

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