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#1 Re: This is Cool » A Geometric Interpretation of i^i » 2014-01-26 14:35:49

Yes!  We most definitely have a deal.  Thank you, I appreciate it very much.

Although I tend to agree with you about the concept of "reasonable men" they do exist, although rare.  And a man who can maintain reason in the presence of confrontation rarer still.  May we have many more grow into that skill.

Speaking philosophically, one of my own tenets is "everything happens for a purpose".  I think our conversation and its resolution will ultimately lead to my offering the ebook free of charge to everyone.  I do believe that I'm not bragging and that my claims will be verified.   

So then, some questions:
1) Ok to reinsert the links in the above post?
2) Ok to repost the first one?  I'll make it clear that the ebook is free of charge for MathIsFun readers in each post where relevant.
3) In trying to insert images I'm getting the message "...sorry, ....only established members ...etc." At which point will I be able to do this?

I will make another post soon.  This one on: Closed Surface Functions in 3Di Coordinates.  That one will also have a link to a blog article of mine illustrating the equations and surface graph.  In the blog I will post a link back to this forum and do the same for each blog illustration that stems from a topic I post here.  Satisfactory?

Thanks!

#2 Re: This is Cool » A Geometric Interpretation of i^i » 2014-01-24 17:17:31

Thank you bobbym for your input.

I used the word objection for two reasons.  First, you asked about other forums.  The same post above is on the Drexel Math forum with the links intact.  So obviously different moderators are interpreting the rules differently.  And if different moderators (or forums) are interpreting the rules differently then they must be based in either personal or different policy objections. 

Second, where you say:

bobbym wrote:

Your first post is nothing but abstracts from your book. This is advertisement for profit or as it is commonly called "spam". I have removed it.

This is inaccurate.  The two abstracts and their links do not refer to the eBook but to my blogs which are full articles with dozens of graphs and animations illustrating the new coordinate system.  And, of course, they are free, as I said previously.  One need not even know about the eBook to make good use of these blog articles.

Further, there are currently 9 blog articles.  The abstracts in my first post refer to two of them and together contain nearly a hundred line graphs and animations.  Clearly it is not possible to post this much information on this forum so setting up the free blog articles and referencing them here seemed a reasonable approach.  If you have a better idea then I am happy to hear it.    Or, I would also be happy to reword the post in any way that you feel would be right.   

I would like to take the conversation a step further.  Most definitely, profit is not the priority.  The eBook contains an amazing array of new material not seen before.  It is the result of a project that I have been working on for nearly thirty years.  Placing it for sale seemed reasonable simply because of its great value.  But it is possible that the eBook is important enough that I should offer it for free in the spirit of science or "new findings" or in donating time as you suggest.  This is a question that I have had and one reason I haven’t looked for a publisher.  I would be interested in yours and any others opinions about this and would be happy to send the complete eBook .PDF file to you or anyone who would be willing to look at it and offer an opinion.

Anyone who would like to do so can write to me and I will send the eBook to them.  My email address is:  gregehmka4dii at gmail dot com

Whether anyone reads it or not, if there is some  consensus that the eBook should be offered for free to anyone and everyone that will answer my question and I will do that. 

As you will see, my eBook A Three Dimensional Coordinate System for Complex Numbers is a breakthrough event and perhaps even a revolutionary one.  I am only looking for the best approach in presenting it.

Thank you very much.

#3 Re: This is Cool » A Geometric Interpretation of i^i » 2014-01-22 12:33:23

The articles that I'm linking to are part of my blog and are completely free and totally interesting.  Please tell me exactly what you are objecting to.  Thanks.

#4 This is Cool » A Geometric Interpretation of i^i » 2014-01-21 07:30:06

gregehmka
Replies: 20

This post is about transcendental functions in the new 3Di coordinate system.

Algebraically and numerically  i^i is equal to e^(-pi/2). But, geometrically each can be interpreted as a point in two different coordinate systems which will place them in two different locations in space as follows:

If we define, what might be called, a ‘four dimensional function’ with one complex number input and one complex number output, of the form:

y + iz = f(x + iT)     (T = theta)

and each of the four variables has a precise geometric meaning:

(horizontal axis, vertical, depth, rotation) = (x, y, iz, iT)

then, taking Euler’s Identity as an example:  e^ipi = -1  specifies a point in “3Di Coordinates”!  This occurs as follows:

y + iz = e^(x + iT)  with  x = 0 and T = pi

-1 = e^ ipi

So the specified point is:

(x, y, iz, iT) = (0, -1, i0, ipi)

Similarly, with a modification to the coordinate system, making the x-axis imaginary and the rotation real, i^i  specifies a point in:

(horizontal, vertical, depth, rotation)  = (ix, y, iz, T)

So the specified point is:

with input T = 0 and z = 1:   ix + y  =  i^(T + iz)  then  (ix, y, iz, T) =  (0, i^i, i, 0)

The e-base generates a rotation of the usual exponential function and is an imaginary rotation about the x-axis and through the depth axis.  The multi-valued nature of the logarithmic function is due to this rotation or at least can be interpreted as such. 

And the i-base exponential function generates a rotation of an ‘i-base imaginary exponential function’ which is a real rotation about the iz-axis.

Going back to i^i equals e^(-pi/2):

i^i is the point:

(h, v, d, r) = (ix, y, iz, T) = (i0, .20787958, i, 0)

and e^(-pi/2) is the point:

(h, v, d, r) = (x, y, iz, iT) = (-pi/2, .20787958, i0, iT)

Both points have the same y-coordinate value which is real but one is on the depth axis and the other is on the horizontal axis.

See:  Link: gregehmka.com/blog/a-geometric-interpretation-of-ii
for the graphs of these two points and their associated functions and coordinates.

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