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Note to AP: When you propose and later publich a "proof" of some mathematical conjecture, you should first state the theorem or conjecture you are trying to prove. Don't assume that this audience already knows exactly what these theorems atate.

Examples:

"The Collatz conjecture, that I have proved is this: ________________-
"The conic sections, that I have proved, included these: ________________.
"Fermat's Last Theorem, which I have proved, is this: _______________________.

You should state exactly what theorem or conjeture that you have proved.

By the way, I have gone back in mathematical history and have discovered some of the earlier work that led the early mathematical geniuses (including your namesake "Archimedes" to believe that the ellipse is in fact a conic section. I could present their arguments here, if you like. They are based on geometrical arguments, in fact, on analytc geometry.
You might disagree with them, and that is OK. You have a proof that the slant section of a cone is an oval. When you present this, first state the theorem.

That's just my advice.

Cheers!

earle
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On Thursday, June 2, 2022 at 11:29:33 PM UTC-5, Earle Jones wrote:
> *
> Note to AP: When you propose and later publich a "proof" of some mathematical conjecture, you should first state the theorem or conjecture you are trying to prove. Don't assume that this audience already knows exactly what these theorems atate.
>
> Examples:
>
> "The Collatz conjecture, that I have proved is this: ________________-
> "The conic sections, that I have proved, included these: ________________..
> "Fermat's Last Theorem, which I have proved, is this: _______________________.
>
> You should state exactly what theorem or conjeture that you have proved.
>
> By the way, I have gone back in mathematical history and have discovered some of the earlier work that led the early mathematical geniuses (including your namesake "Archimedes" to believe that the ellipse is in fact a conic section. I could present their arguments here, if you like. They are based on geometrical arguments, in fact, on analytc geometry.
> You might disagree with them, and that is OK. You have a proof that the slant section of a cone is an oval. When you present this, first state the theorem.
>
> That's just my advice.
>
> Cheers!
>
> earle
> *

Hi Earle I appreciate your advice, but I use Usenet mostly as preliminary, as loose talk. I do not much care in being polished on Usenet-- saving the polishing for publishing.

I go under the suspicion that whatever I post to Usenet, and not understood by a audience, is that such an audience is -- not worth reaching for me-- in the first place. For their remarks or replies or probably a total waste of my time.

In my published book of Collatz, in fact I state the Collatz in the preface-- even before the first chapter-- which you would much appreciate. Here in Usenet, I am as informal as possible for Usenet is a recording platform for me.

As for your ideas of Archimedes, my reincarnated self-- I doubt that he spent much time with curves other than figuring out pi.

I am almost sure that Archimedes spent little to no time on oval. And not sure if Appolonius spent much time on oval versus ellipse. I find no "history of the oval".

And even some books say oval has no definition.

I think the history of oval is that the Ancient Greeks saw it as a misshappened ellipse, and the ellipse as a misshappened circle.

The Ancient Greeks seldom experimented with hands of these objects. And Apollonius never discusses the oval, never discusses symmetry. There is a difference in what modern math historians say what happened and what actually happened.

On Thursday, June 2, 2022 at 11:29:33 PM UTC-5, Earle Jones wrote:
> *
> Note to AP: When you propose and later publich a "proof" of some mathematical conjecture, you should first state the theorem or conjecture you are trying to prove. Don't assume that this audience already knows exactly what these theorems atate.
>
> Examples:
>
> "The Collatz conjecture, that I have proved is this: ________________-
> "The conic sections, that I have proved, included these: ________________..
> "Fermat's Last Theorem, which I have proved, is this: _______________________.
>
> You should state exactly what theorem or conjeture that you have proved.
>
> By the way, I have gone back in mathematical history and have discovered some of the earlier work that led the early mathematical geniuses (including your namesake "Archimedes" to believe that the ellipse is in fact a conic section. I could present their arguments here, if you like. They are based on geometrical arguments, in fact, on analytc geometry.

Yes, go ahead and present some of that history of oval-- for I have not found anything connecting Apollonius connecting Archimedes with the study of Oval. I would really like to see what those Ancient Greeks thought of "symmetry" for the cone and oval have 1 axis of symmetry , yet ellipse has 2, and why Apollonius made that bad mistake of thinking ellipse was slant cut. Apparently Symmetry was never a big deal in Ancient Greek times. Perhaps it was never even introduced into mathematics until after the Greeks. Come to think of it, I recall no Euclidean Geometry proof or lessons on symmetry. Symmetry does not appear in science until Leonardo painting of Vitruvian Man. And symmetry does not appear in science in full force until the need to have poles for electricity and magnetism as axes of symmetry.

Does Apollonius even say "cone has one axis of symmetry"? The Cylinder has 2 axes of symmetry. Does either Euclid or Archimedes or Apollonius acknowledge a cylinder has 2 axes of symmetry yet cone only 1. Is there ever a indication in their writings that they knew cylinder 2 but cone 1?

> You might disagree with them, and that is OK. You have a proof that the slant section of a cone is an oval. When you present this, first state the theorem.
>
> That's just my advice.
>
> Cheers!
>
> earle
> *