# Spin Relativistic

## Horn spheroid golden mean model as relativistic magnetic flux manifold for the electron

golden ratio horn spheroid,
angle 54.7°
between trajectories and axis (at equator)

view also spin and
magnetic moment vectors (in different perspectivic depictions)

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

Active publication material, Jan 2020. Hellenic Mediterranean University

contact:
markoul@chania.teicrete.gr

similar trajectories **7 : 6** / on
**sphere**

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

animations by
w. daeumler (
artmetic /
horn torus )

parametric form for trajectories above:

x = (r/Φ)·(1 − cosφ)·cos(1.1441φ ∓ Δω)

y = (r/Φ)·(1 − cosφ) · sin(1.1441φ ∓ Δω)

z = r·sinφ Φ = 1.618 (golden ratio)

φ is the poloidal angle, 2n·π at spheroid center

Δω = Δω(t) makes artificial rotation around axis