# When did I find the first exponential circle in 3D space?

It was in the Spring of 2013 when I was walking in a nearby park when it suddenly dawned on me that this exponential process that ran through the basis vectors (1, 0, 0), (0, 1, 0) and the z-axis unit vector (0, 0, 1) was periodic.
It could not be anything else because I was capable of calculating the logarithm of the first imaginary unit j.

I remember at first I just did not have a clue it would be a circle, I even had vague fantasies like may be it is a vibrating string where all those string physics professors talk about.

Now this evening I was just Googleing around a little bit when I came across this picture again:

It dates back to 30 May 2013 and I used this picture as a joke about how professional math professors look in my fantasy world. Within a week I found that the 3D complex periodic curve was in fact a circle.
So I had to laugh hard about my own joke once more because if I had known the 3D periodic thing would also be a circle I would have made the joke very different… Because one way or the other this picture now also represented me.

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You know this last week I am a bit puzzled by what the next post should be, in December 2013 I conducted a good investigation into the roots of unity related to the two exponential circles and because every body knows roots of unity it would a nice started for this website.

On the other website you can find it at the 05 Jan 2014 entry:

http://kinkytshirts.nl/rootdirectory/just_some_math/3d_complex_stuff02.htm#05Jan2013

At the time I was amazed with all the things you can do with the eigen values of the imaginary components j and j squared. From diagonalization to the roots of unity, my theory got definitely air born.

Later in January 2014 I found a new Cauchy integral formula (actually two just like I found two sets of roots of unity each for the admissable forms of 3D multiplication). Also in Jan 2014 I cracked the problem of 5D complex numbers.

By all standards, as far as I can see it; the two months Dec & Jan in that time were the most productive ever.

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Now, almost 3 years later finally stuff on Google take off, for example if this day I start searching for the phrase 3dcomplexnumbers it returns back three results from this new website.
Just look at the next screen shot picture:

So after waiting all these years, finally I begins to look as if stuff starts getting air born on some  bigger scale than before.

Ok, end of this update. As usual till updates!

# Just a background picture plus some bla bla bla.

About 10 days ago I took a look at how much pictures I have crafted since the beginning of this website and I decided to take a nice holiday.

So in this update no hardcore math or softcore math, I want to show you just a background picture and talk a bit about that. Here is the picture:

For the human brain if you see things of similar shape but one is smaller compared to the other, most of the time the thing that looks small has a greater distance from where you are.
Of course there are deviations from this: When you see a child standing before a grown up you simply observe a small person standing before a larger one.

Now look carefully at the picture above, constantly the larger things are beyond those one layer smaller and constantly if it is one layer smaller it looks like the lean on the larger one.

It was years ago that by accident I found this kind of stuff, for myself speaking it looks beautiful because it transports your brain instantly into two directions:

1. The smaller things should be further away &
2. The smaller things lean on the larger ones so they should be closer…

So this gives a nice discrapency in the brain of the reader, what vision will prevail or will there be some circular insight like a cat trying to catch it’s own tail?

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In another development I crafted reason number 24 as why electrons and stuff like that are the long sougth magnetic monopoles, here is a teaser picture for that (click on it to land on the other website on the page about magnetic stuff):

Ok, that was more or less what I had to say today.

# Correction number 2 on the 6D complex numbers.

Three months ago on 06 Dec 2015 I posted the 6D numbers update because that is the smallest space that includes both the complex plane and my own invented 3D complex numbers.

To my amazement a few days ago I typed in on a Google search the phrase ‘3d complex numbers’ and when you search for pictures my teaser picture for that 06 Dec post was picture number 3.

So I started reading my own stuff again; why is this post so popular given the fact it has an extremely boring title???

It was only later that very likely my own goal of including stuff that is known, like the complex plane, must be some factor for readers clicking on that post so often. And after thinking about it coming back & so on & so on.

But I found another typo in that old post and that is the update for today; I show you the part that includes the typo and also show you the correction. Picture number 3 shows the teaser picture standing on rank 3 in the Google picture search.

Now you must never think you are king with search results like this, if for example you are in Brazil and type in the same search string ‘3d complex numbers’ you might very well get a very different result: Google like to ‘craft the search to the individual’ in order to maximize advertisement revenue…

Anyway, three pictures that form a correction on the 06 Dec post are below:

The above picture contains the stupid typo that says this imaginary number l is the square root of the complex plane thing i. This is plane stupid, in the next picture you see a correction±

In the third picture of this update you see the teaser picture on position number 3 in that Google picture search, don’t forget Google has a large bag of tricks to localize search results. So I as the idiot that I am might think that in spaces like Brazil or Australia you get the same results I forgot how Google makes the money: