# 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:

The song of omega reloaded
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!