WOLFRAM|DEMONSTRATIONS PROJECT

Complexified Pseudosphere

​
real/imaginary part
parametrization change parameters:
α
β
γ
δ
parametrization parameter ranges:
φ-Range
ϑ-Range
The parametrized surface
r(ϑ,φ)={x,y,z}=Re({ϑ-tanh(ϑ),cos(φ)sech(ϑ),sin(φ)sech(ϑ)})
is called a pseudosphere. This Demonstration plots a linear combination of the real and imaginary parts of
r

(ϑ,φ)
, where
r

(ϑ,φ)=r(αϑ+β,γφ+δ),
where
α,β,γ,δ∈
.