RE: [gts-general] [RFC] Rational Trig

[Gary R. V. S. <g.r...@wo...>]

> From: David Sterling
> Sent: Tuesday, September 20, 2005 11:02 AM
> To: gts...@li...
> Subject: RE: [gts-general] [RFC] Rational Trig
> 
> 
> The presentation style left me a little skeptical as well, 
> but I'm tempted to browse through a copy when it comes out. I 
> personally think the Calculus is a stunningly powerful set of 
> tools

Yeah, it's worked pretty well since about Newton's time, hasn't it? ;-)

> and to attempt to rework bits of mathematics to avoid 
> using it for practical (as oposed to pedagogical) purposes is 
> a bit like trying to redesign vehicles for transcontinental 
> travel without using the wheel.

BUT THE WHEEL IS A CIRCLE!!!  IT'S CONFUSING!!!  AND SINCE IT IS CONFUSING,
IT MUST BE FUNDAMENTALLY FLAWED!!!!

;-)

> That said, this chapter gives 
> a sense that we could sucessfully define Euclidean geometry 
> using squared distance and (roughly) ratios of sides of 
> triangles( and some of us might even find it asthetically 
> pleasing).

There's a lot of things "We could" do.  For approximately a billion years,
generation upon generation of "We"s much smarter than the good Doctor or
anybody here have successfully applied angles and lengths to all manner of
problems, and haven't worried much about it.  And despite the good Doctor's
ramblings, no, the square of a distance is not more intuitive than the
distance itself, nor is that "spread" of his more intuitive than the
omnipresent angle.

> I suspect these ideas become more compelling when 
> studying Euclidean geometry over more general fields, or in 
> number theoretic applications where there is genuine insight 
> to be gained from understaning the origin of particular 
> irrational numbers.
> 

Maybe they is and maybe they ain't.  Last night, I would have rated what
I've seen of the treatment provisionally at maybe 50% burger, 50% bun.
After sleeping on it, and after having read this article:
http://physorg.com/news6555.html
I am willing to bet anybody a Coke that it's 99% Kookdom, 1%
Semi-Interesting Mathematical Diversion Which Breaks No New Ground.  And
before you take me up on that, note what the guy says:

"Generations of students have struggled with classical trigonometry because
the framework is wrong."

"The framework [of 'classical' trigonometry] is wrong" == the statement of a
Kook.

A further bet: his book has a claim somewhere in it that the Pyramids of
Egypt could only have been designed and built using "Rational Trigonometry".
That's a TWO-Coke bet!  You KNOW this guy makes a claim like that! ;-)

> btw: per your comment about rotation matrices and 
> quaternions: Applying these operator doesn't involve 
> trigonmetric functions but defining them sure does :)
> 

I knew I would catch hell for that ;-).

Ok, then let's make it a "spreadular momentum" vector.  Take a rigid body's
"spreadular momentum", its "quadranertia tensor", whatever, and let's see
how the body changes orientation.  I'm guessing the formulation is vastly
more complex than the 'classical' approach, but I would be delerious for the
good Doctor to prove me wrong!

> Just my 2 cents,
> 
> David

-- 
Gary R. Van Sickle
 
> -----Original Message-----
> From: gts...@li...
> [mailto:gts...@li...]On Behalf Of 
> Gary R. Van Sickle
> Sent: Monday, September 19, 2005 6:44 PM
> To: gts...@li...
> Subject: RE: [gts-general] [RFC] Rational Trig
> 
> 
> > From: gts...@li...
> > [mailto:gts...@li...] On Behalf Of Rob 
> > McDonald
> > Sent: Monday, September 19, 2005 7:18 AM
> > To: gts...@li...
> > Subject: [gts-general] [RFC] Rational Trig
> > 
> > This book will soon be released from the land Down Under.  
> > I'm reserving judgement on whether he is crackpot or genius until 
> > after I take a closer look at his book, but I think some of 
> his ideas 
> > certainly have merit.
> > 
> 
> Welp, read the first chapter.  Whenever I see anything to the 
> effect of "why, we just use the length *squared* instead of 
> the length, and the fundamentally flawed concept of 
> trigonometry becomes mere childs' play!", the first thing I 
> ask is: "Well then, how come one of the geniuses you're 
> 'pooh-pooh'ing come up with it?"
> 
> As to any possible applicability to things like GTS, well, 
> I'll have to wait to see how he handles rotations and 
> translations of his triangles without matrices or quaternions 
> before buying his book.  No trig involved in rotating things 
> with matrices or quaternions.
> 
> --
> Gary R. Van Sickle
>  
> 
> 
> 
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