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Measure of the Shell-Thron Region
#1
Question 
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?
ฅ(ミ⚈ ﻌ ⚈ミ)ฅ
Please remember to stay hydrated.
Sincerely: Catullus
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#2
(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. Tongue
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