There are lot’s of reasons for this update; one reason is that the actual calculation is mega über ultra cool. Another important reason is that this collection of plain imitation of how the value for the number i in the complex plane was found serves as a proof in itself that this way of crafting 3D complex and circular numbers is the only way it works.
Don’t forget that on the scale of things the Irish guy Hamilton tried for about a decade to find the 3D numbers but he failed. Yet Halmilton was not some lightweight, the present foundation of Quantum Mechanics via the use of the Hamilton operator is done so via the work of Hamilton…
Wether the professional math professors like it or not; that is the scale of things.
During the writing of this post I also got lucky because I found a very cute formula related to the so called Borwein-Borwein function. I have no clue whatsoever if it has any relevance to my own work on this website but because it is so cute I just had to post it too…
Furthermore I used two completely different numerical applets, one for integration and the other for evaluating the log of a matrix, only to show you that these kind of extensions of the complex plane to three dimensional space is the way to go and all other approaches based on X^2 = -1 fail for the full 100%.
This post is ten pictures long, size 550 x 775 pixels.
At the end I will make a few more remarks and give you enough links for further use in case you want to know more about this subject. Have fun reading it.
In this update you might think that via the pull back principle you observed some proof for the value of the integrals we derived, but an important detail is missing:
In 3D space the exponential circle should be run at a constant speed.
As a matter of fact this speed is the length of the number tau, you can find more insight on that in the theorem named ‘To shrink or to grow that is the question’ at:
On the length of the product of two 3D numbers.
A bit more hardcore is my second proof of the value of the integrals as derived in this post. On 15 Nov 2015 I published the second proof that I found while riding on my bicycle through the swamps near a local village named Haren. It is kinda subtle but you can use matrix diagonalization to get the correct answer.
The reaction from the ‘professional community of math professors’ was the usual: Zero point zero reaction. These people live in a world so far away from me: overpaid and ultra stupid…
Integral calculus done with matrix diagonalization.
A link to the online encyclopedia of integer sequences is the next link.
Remark that by writing the stuff as on-line instead of online reflects the fact this website must be from the stone age of the internet. That is why it can have this strange knowledge…
The On-Line Encyclopedia of Integer Sequences
https://oeis.org/ (Just fill in 1, 2, 0, 9, 9, 5, 7 in order to land on my lucky day).
The last link is one of those pages that try to explain as why 3D complex numbers cannot exist, the content of this page is 100% math crap written by a person with 0% math in his brain. But it lands very high in the Google ranking if you make a search for ‘3D complex numbers’.
So there must be many people out there thinking this nonsense is actually true…
N-DIMENSIONAL COMPLEX NUMBERS.
Ok, this is what I had to say. Let me close this post, hit the button ‘update website’ and pop up a fresh beer… Till updates.