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#1 2014-01-21 07:30:06

gregehmka
Member
Registered: 2014-01-20
Posts: 4

A Geometric Interpretation of i^i

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.

Last edited by gregehmka (2014-01-29 02:41:37)


"Be excellent with one another." - Devsujjan Singh

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#2 2014-01-22 10:56:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,365

Re: A Geometric Interpretation of i^i

Hi;

I have removed all the links because they are advertisements and are forbidden on the forum.

The forum is for member interaction and math posting. We have only volunteers here. Feel free to lend a hand with the spirit of true giving but there will be no more advertisements for profit.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2014-01-22 12:33:23

gregehmka
Member
Registered: 2014-01-20
Posts: 4

Re: A Geometric Interpretation of i^i

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.


"Be excellent with one another." - Devsujjan Singh

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#4 2014-01-22 20:23:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,365

Re: A Geometric Interpretation of i^i

what you are objecting to

It does not matter what I object to and who said I was objecting to anything? Those are the rules.

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.

Your site is also dedicated to the selling of your book. This is fine but why do you imagine that you can advertise in here?  I notice your site is spam free. May I post, "Eat at bobbym's 3.95" over there? If you came out tomorrow morning and found neatly lettered on the side of your car my advertisement "bobbym's hotdogs 1.00." Would you not call the police? Why do wish to use our space for your business ventures? Do you not have a publisher? He is being paid to advertise your material.

Why is this the only math forum I see that has this advertisement? Is it because it has been removed?

This space is for forum interaction and mathematics not for advertising for profit. We have mathematicians, physicists, engineers, teachers and myself all donating their time for free, you should try it too.

The best way to prove that your methods are better is by solving problems over here showing that your methods lead to quicker solutions, or solve intractable problems, or make programs run faster, or are more elegant etc. That is the sort of advertising that is useful and encouraged.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#5 2014-01-24 17:17:31

gregehmka
Member
Registered: 2014-01-20
Posts: 4

Re: A Geometric Interpretation of i^i

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.

Last edited by gregehmka (2014-01-26 14:37:16)


"Be excellent with one another." - Devsujjan Singh

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#6 2014-01-24 18:31:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,365

Re: A Geometric Interpretation of i^i

Hi;

So obviously different moderators are interpreting the rules differently.

I would assume that different people would interpret anything differently. They may not be a moderated forum. They may have different rules, I do not know.

Or, I would also be happy to reword the post in any way that you feel would be right.

I have already fixed it according to the rules we have here.

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.

You have used many phrases and superlatives such as amazing, great value, interesting, important enough etc. You have cleverly worked in phrases like spirit of science or "new findings", "breakthrough event and perhaps even a revolutionary one." My point is you have already got a fair amount of advertising of your book.  Why do you even need the links? Isn't that what Google is for?

The only thing that could excuse such comments is if you are right. If your viewpoints are right then you are not bragging.

gregehmka wrote:

Anyone who would like to do so can write to me and I will send the eBook to them.  My email address is:  gregehmka 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.

The above quote removes the problem.

It is said that any problem can be resolved among reasonable men. To me, using reasonable and men in the same sentence is not reasonable.

I believe in the concept of risk versus rewards. If I allow the material then the risk is my reputation for doing a good job in short, my integrity. The rewards are these:

1) I will ask that you provide a link to this forum on your site.

2) You will make available to any member of this forum who asks to see your book free of charge as you promised.

Do we have a deal?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#7 2014-01-26 14:35:49

gregehmka
Member
Registered: 2014-01-20
Posts: 4

Re: A Geometric Interpretation of i^i

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!


"Be excellent with one another." - Devsujjan Singh

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#8 2014-01-27 03:06:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,365

Re: A Geometric Interpretation of i^i

Hi;

Yes, to 1 and 2.

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?

That is an established rule and I can do nothing about it. It will happen after a certain number of posts and a certain amount of time both of which are unknown even to me. In the meantime ask me and I will post the picture for you until you can post your own.

Satisfactory?

Okay.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9 2014-01-27 18:09:32

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,663
Website

Re: A Geometric Interpretation of i^i

What advertisement was removed?

Eat at bobbym's 3.95

Thats a little to expensive, don't you agree?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#10 2014-01-27 22:39:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,365

Re: A Geometric Interpretation of i^i

Hi Agnishom;

You came in at the end of the movie.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#11 2014-01-27 22:46:50

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,663
Website

Re: A Geometric Interpretation of i^i

Yes, I think I have missed a lot


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#12 2014-01-28 00:09:11

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,380

Re: A Geometric Interpretation of i^i

Agnishom wrote:
bobbym wrote:

Eat at bobbym's 3.95

Thats a little to expensive, don't you agree?

But there are too many unknowns.

eg.  What currency is this?

eg.  Just how much can you eat for that price?  It might be an all day, eat all you want, diner.

I was certainly tempted by the offer.  Which just goes to show the power of advertising.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#13 2014-01-28 00:26:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,365

Re: A Geometric Interpretation of i^i

I can answer those questions. It is $3.95 American money which is very cheap. It is an all day and all you can eat place but the cook is sort of on the surly side. He has been known to chase people around with a baseball bat when they criticize the food. Slow customers have been bludgeoned while begging for mercy. Repeated shock therapy has only increased his viciousness and patrons would do well to wear head gear while eating there.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#14 2014-01-28 01:18:29

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,380

Re: A Geometric Interpretation of i^i

hi bobbym,

Is this the guy?  I've seen him before.

Bob

View Image: john cleese.jpg

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#15 2014-01-28 03:06:36

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,663
Website

Re: A Geometric Interpretation of i^i

Hi bob;

Do you know who Sir Suman  is?

Hi ym;

Do you sell Onions?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#16 2014-01-28 04:32:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,365

Re: A Geometric Interpretation of i^i

Is this the guy?  I've seen him before.

I have too. Looks like a Monty Python skit.

Do you sell Onions?

Nope and I have not had them in a while.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#17 2014-01-28 04:38:21

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,663
Website

Re: A Geometric Interpretation of i^i

Pistachios? Boats?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#18 2014-01-28 04:41:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,365

Re: A Geometric Interpretation of i^i

I will tackle the mighty Everglades in a kayak.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#19 2014-01-28 04:50:01

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,663
Website

Re: A Geometric Interpretation of i^i

1) I will ask that you provide a link to this forum on your site.

Isn't that advertising too?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#20 2014-01-28 06:37:31

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,380

Re: A Geometric Interpretation of i^i

Agnishom wrote:

Do you know who Sir Suman  is?

No.  And my friend, Mr Google, has many, many listings.

Will you enlighten me?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#21 2014-01-28 14:11:48

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,663
Website

Re: A Geometric Interpretation of i^i


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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