# Spin Relativistic

## Horn sphere model as relativistic magnetic flux manifold for the electron

( → more
explanatory version )
stop this animation ↑

© Emmanouil Markoulakis, no permission for any use, distribution or modification.

Active publication material, March 2020. Hellenic Mediterranean University

contact:
markoul@chania.teicrete.gr

→
**horn spheroid** golden mean model

see also EM's
**model of the atom**

animations by
w. daeumler (
artmetic /
horn torus )

parametric form for the trajectories above:

x = r·(1 − cosφ)·cos(φ·√2 ∓ Δω)

y = r·(1 − cosφ) · sin(φ·√2 ∓ Δω)

z = r·sinφ →
definition of φ

Δω = Δω(t) makes artificial rotation around axis

to get __one__ continuous trajectory with 22 loops

√2 is approximated by rational number 31/22