Advice and general guidance on writing and submission of a math paper?

[Pejeu]

What can it be about? How do we ascertain the novelty of the intended paper?

How should it be structured?

Where should it be submitted and how?

What can it be written in and what format should it be forwarded in?

Any advice is appreciated. Thank you.

 

[ZapperZ]

What can it be about? How do we ascertain the novelty of the intended paper?

How should it be structured?

Where should it be submitted and how?

What can it be written in and what format should it be forwarded in?

Any advice is appreciated. Thank you.

Don't you have an academic advisor or a supervisor that you can ask this to?

Many of the questions you asked tend to be journal-specific. The structure and the format are two such examples. Each journal has its own requirement on not only the format and structure, but also the level of "novelty" or importance of the content. An experienced, senior researcher in a particular field will know where something should be submitted to to get acceptance.

Otherwise, what you'll get out of something like this are rather superficial responses.

Zz.

 

[Pejeu]

Not really. I'm out of school. Doing math more as a hobby.

My long term goals are an analytical solution to the area of overlap between two random triangles on the plane and a more general analytical solution to the area of a quadrilateral, that returns the enclosed area irrespective of whether it is self-intersecting or not.

I have an approach planned for the latter and suspect it might enable me to solve the former as well.

 

[ZapperZ]

Not really. I'm out of school. Doing math more as a hobby.

Which was what I suspected, and you know why?

The fact that you asked such questions implied that you haven't read many (any?) math papers, and thus, are quite possible that you are unaware of the body of knowledge in that field. This, more than anything else, should ring warning bells all over the place, especially when you think that you may have something publishable.

We get these kinds of questions rather often from amateurs who think they have discovered a plethora of things. I don't recall any of them having amounted to anything worthwhile. If you haven't read enough math papers to not know what is required from a journal for publication, chances are, you do not know what has been happening in a particular subject matter. You might want to consider the possibility that you might be wasting your time. Otherwise, if you strongly believe that you have something, then rather than already aiming for a publication, have an expert look at it first before attempting to submit to a journal. Journal editors see this type of submission A LOT, and unless you want to waste your time doing something will be rejected outright, you need to do your own homework.

Zz.

 

[Pejeu]

The two objectives (triangle-triangle area of overlap and enclosed area of a self-intersecting quadrilateral) I mentioned earlier I'm pretty sure have not been tackled yet. Not analytically, in any case. More like almost certain.

So in that sense I already did my homework and it really seems to me this is new ground.

But how would I go about really checking the novelty of my ideas so as to be certain (not almost) that I'm treading new ground?

I mean a good way to know. Not asking someone in the field.

Cause there is no-one (that I know) in the field of analytical overlap geometry. I don't think there even is such field.

And I don't know anyone who could be qualified an expert on analytical solutions to the areas of self-intersecting polygons either.

Where could I enlist the help/guidance of such experts?

Look it up on arxiv.org? Did that, nothing.

It's like such problems are too basic to even register with professionals even though they seem fundamental to me.

An analytical solution to triangle-triangle overlap, for instance, would have immediate, extremely useful applications.

From a trivial view frustum test to exclude all triangles that have no area in common with the screen rectangle to raster image resizing, collision detection and so on.

Also, the path to an analytical solution to tetrahedron-tetrahedron common volume would then be foreseeable. Which would have even greater implications for collision detection.

I really don't think such works, successfully completed, wouldn't amount to anything. Even if the papers they're espoused in are written by foot.

People used to do math much less formally centuries ago and yet their work isn't discounted for it. It does amount to something, even if it wasn't typeset in latex but rather penned in ink and feather.

 

[ZapperZ]

The two objectives (triangle-triangle area of overlap and enclosed area of a self-intersecting quadrilateral) I mentioned earlier I'm pretty sure have not been tackled yet. Not analytically, in any case. More like almost certain.

So in that sense I already did my homework and it really seems to me this is new ground.

How can you tell? Have you done an extensive literature search of the journals? You appear to not have done so or else you would have been aware of (i) the format and structure of the papers in that field, (ii) the EXPERTS in such fields since you would have at least names of people who published in that area, and (iii) the journals that would publish such topics.

That is how you would check the novelty of your idea.

And if you claim that there's no one who is an expert in what you are working in, then who do you think is going to referee your work when you submit it to a journal? If the journal finds no one who would do that, your submission will be kicked out.

Or are you claiming that you single-handedly have invented a new topic in mathematics?

Zz.

 

[Pejeu]

You're right, my work is basically a development in geometry. I should send it to a geometry journal.

I looked up DOAJ and came up with the following candidates:

Balkan Journal of Geometry and Its Applications
http://www.mathem.pub.ro/bjga/

Forum Geometricorum:
http://forumgeom.fau.edu/index.html

Global journal of advanced research on classical and modern geometries:
http://gjarcmg.geometry-math-journal.ro/

Journal of Computational Geometry:
http://jocg.org/index.php/jocg

Journal of Mathematical Physics, Analysis, Geometry:
http://jmage.ilt.kharkov.ua/mag_e.html

SYMMETRY, INTEGRABILITY and GEOMETRY: METHODS and APPLICATIONS
http://www.emis.de/journals/SIGMA/

Are you familiar with any of them? Any suggestions as to which I should submit to?

Maybe a new subfield in geometry.

 

[Vanadium 50]

Are you familiar with any of them? Any suggestions as to which I should submit to?

You should read a few issues of each and decide which is the most relevant.

Scientific literature is a dialog. Publishing without reading is tantamount to talking without listening. People won't be impressed.

 

[Jorriss]

When you say area of overlap between two triangles, do you mean something like the following:
http://math.stackexchange.com/questions/154628/find-the-area-of-overlap-of-two-triangles

 

[Pejeu]

Yes. Exactly. That guy's after the same exact thing. The suggestions he gets are for algorithmic solutions, though.

You need to test for intersections, parallel edges and such. It's ugly.

You can actually implement discontinuous functions without using decision blocks. By using abs() and trunc().

You can implement the sign function in this manner. As well as floor() and ceil(), min() and max() and others (lowest multiple greater than etc).

For example the length of overlap between two segments on a line can be given by:

$${{\left | A - D \right | - \left | B - D \right | + \left | C - B \right | - \left | C - A \right |} \over {2}}$$

Where A and B are the position on the axis of the endpoints of the first segment and C and D of the second segment.

 

[Jorriss]

Yes. Exactly. That guy's after the same exact thing. The suggestions he gets are for algorithmic solutions, though.

I can appreciate you working on this independently, but I found that after only a few seconds of a google search. You really should do a thorough literature search and you could not have done one if you are asking what journals are best to submit this to.