# 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