Measure of the Shell-Thron Region

[Catullus]

What is the area of the complex part of the Shell-Thron region?
What about the measure of the 8 dimensional measure of the octonion Shell-Thron region?

[JmsNxn]

What is the area of the complex part of the Shell-Thron region?
What about the 8 dimensional measure of the octonion Shell-Thron region?

The boundary of the shell thron region is traced as:

\[
\gamma(\theta) = \exp\left(e^{i\theta-e^{i\theta}}\right)\\
\]

So pull out your double integral:

\[
\int\int_{\mathcal{S}} 1\,dA\\
\]

Get calculating, we can't do everything for you... Doubt there's a closed form, but you might be able numerically evaluate.