+- Tetration Forum (https://tetrationforum.org)
+-- Forum: Tetration and Related Topics (https://tetrationforum.org/forumdisplay.php?fid=1)
+--- Forum: Mathematical and General Discussion (https://tetrationforum.org/forumdisplay.php?fid=3)
+--- Thread: Measure of the Shell-Thron Region (/showthread.php?tid=1570)
Measure of the Shell-Thron Region - Catullus - 07/09/2022
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?
RE: Measure of the Shell-Thron Region - JmsNxn - 07/10/2022
(07/09/2022, 05:46 AM)Catullus Wrote: 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.
