🧵 Notes on the Cubit
Anonymous at Tue, 15 Oct 2024 19:33:18 UTC No. 16433365
Further studies upon the cubit reveal a startling revelation. namely that [math]\frac{\phi^2}{5}[/math] is the truer cubit than [math]\frac{\pi}{6}[/math] this is because
[math]\frac{\sum_{n=0}^{\infty}\fra
and
[math]\sum_{n=0}^{\infty} \frac{\phi^n}{2^n} - \frac{\phi^2}{5} = 0 [/math]
what gives this equation meaning is its source derivation, that the sum of the ratios of the volumes of the n-sphere to the n-cube converge to [math]\odot[/math] the true value for the egyptian royal cubit.
This thinking stems from not considering pi as a constant, but rather a generalizable property of R^2, much how like the curl is only applicable to R^3 in vector algebra. We need the analogue of geometric algebras interior and exterior products. This, i propose to define that the unit n-sphere possesses a radius of [math]\phi^{-1}[/math] and that pi float to accommodate this constraint. For clarity we say [math]\pi_n =[/math]
In our previous study we sought the volume of n-sphere without assuming a constant value for [math]\pi[/math] after all, this constant is derived from 2-space, and not generalizable in n-space. We instead approach the problem by considering the ratio of the n-sphere to the n-cube with 1 critical assumption, that
[math]\odot = \frac{V_{n-sphere}}{V_{n-cuboid}} = \sum_{n=0}^{\infty}\frac{\phi^n}{2^
We can than derive a sort of dimensionally attuned constant for pi, for example in R^3.
[math]pi_3 = 18 + 6\sqrt{5}[/math]
which is good to regular pi to 0.0000481
[math]\frac{\sum_{n=0}^{\infty}\fra
[math][/math]
[math]\sum_{n=0}^{\infty}\frac{\phi
[math]\sum_{n=0}^{\infty}\frac{\phi
https://warosu.org/sci/thread/16406
Anonymous at Tue, 15 Oct 2024 19:40:05 UTC No. 16433374
This isn't your average everyday schizoposting.
This is ADVANCED schizoposting.
Anonymous at Tue, 15 Oct 2024 19:45:26 UTC No. 16433378
>>16433365
addendum [math]\odot[/math] was often left without a division by 10
[math]\frac{\sum_{n=0}^{\infty}\fra
[math]\frac{\sum_{n=0}^{\infty}\fra
Anonymous at Tue, 15 Oct 2024 21:30:25 UTC No. 16433460
>>16433374
I find it quite intriguing it stemmed from following a simple mathematical coincidence in pic related, in the amusement of a mathematician, i would assert this https://www.wolframalpha.com/input?
The intensity of the procedure deepened and lo and behold does a n-dimensional series emerge. Lets consider the 2-d case.
[math]A = \pi r^2[/math]
[math]1^2 = \pi r^2[/math]
[math] \sqrt{\frac{1}{\pi}}= r[/math]
now, setting r to [math]\frac{1}{\phi}[/math] we infer pi from this mathematical coincidence
[math] \sqrt{\frac{1}{\pi_{new}}}= \frac{1}{\phi}[/math]
we find that, this new pi for 2d is
[math]pi_{new} = \phi^2[/math]
now, amazingly this same condition arises in the nth dimension namely
[math]V_n = \phi^n r^n[/math]. Its rather cathartic, we see in the n-series rather arcane coefficients, for example why [math]\frac{4 \pi}{3}[/math] in [math]V_{3-sphere}=\frac{4 \pi}{3}r^3[/math] or [math]\frac{\pi^2}{2}[/math] in R^4 . Performing this trick with of setting [math]\pi_{n}[/math] with the unity volume and the inverse golden radius, cancels them all out, for example [math]\pi_4=\frac{\phi^2}{2}[/math]
which infers perhaps a unique perspective on what the n-sphere series perhaps aught to be, or how to interpret volumes of 1d and 0d objects.
we than laugh as we take the series of [math]\pi_{n}[/math] and it actually converges right back into itself. that
[math]\odot = \frac{V_{n-sphere}}{V_{n-cube}} = \sum_{n=0}^{\infty} \frac{\phi^n}{2^n}[/math] which goes right back to [math]\frac{\phi^2}{5}[/math]