Elliptical Spheres
Elliptical Spheres
Elliptical spheres are neither spheres nor elliptic. Elliptical spheres are complex vectors such that and , , are elliptic functions. A possible parametrization of these vectors is given through Neville theta functions as
r={x,y,z}
r.r=1
x
y
z
r
α,m
1
1-m
ϑ
n
ϑ
n
1-m
m
ϑ
s
ϑ
s
m
ϑ
c
ϑ
c
ϑ
d
ϑ
d
z∈
α∈
m∈
In this Demonstration, runs over part of the complex plane and and are complex parameters. The graphic displays variable relative fractions of the real and imaginary parts of , , and .
z
α
m
x
y
z