New Trigonometry
According to this PhysOrg writeup, a Prof. Wildberger has published a new book which redefines trigonometry into what he calls Rational Trigonometry, doing away with all trigonometric functions and angles. Instead he’s replaced the concept of distance with Quadrature (Q(x1,y1,x2,y2) = (x2-x1)^2+(y2-y1)^2, essentially the distance formula without the square root) and angle with Spread (the ratio of two lines’ separation as quadrature measured from a triangle formed between an arbitrary point on one line and its corresponding projection on the other line). Then he’s written a whole book providing a full course of trigonometry instruction without using sine, cosine, tangent or any of those difficult-to-exactly-solve concepts. Chapter one is on-line here.
You have to admire this man’s gall, attempting to rewrite trigonometry courses’ teaching strategies the world over.
There are some benefits to his method of expressing trigonometric formulas: since the trigonometric functions do not have many exact solutions, by doing 3D math in terms of Spread and other ratios we can (theoretically) improve mathematical accuracy, at least without the hassle of keeping a high-resolution cosine lookup table nearby when doing discrete mathematics…
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I’ve looked at it, and it’s a variation on the stadard system that is IMO confusing for everyone who learned the “proper” way. Since it’s too different and works in a fashion that few people understand, it’s going to be difficult getting it anywhere near mainstream. I, for example, know that descriptions and calculation notes in surveying aren’t going to be accepted under this sort of workout. So maybe it’s nice as an easy way to make math incapable Lib. Arts majors learn, but other than that it’s nothing.
It’d be taught in high school, not college/university… At least I hope everyone learns trig in middle or high school!
Well see, if it’s taught this way in high school, then there’s now a generation of people in this one particular school or other that have learned it the “new” way, and when they get to college and want to do something serious, now they have to relearn it the “old” way because that’s what everyone else uses for serious work. So, it doesn’t matter how you slice it, this sort of thing is not good for serious professionals IMO who will use trig, hence my comment that it would be good for the mathematically incompetent getting lame brain soft degrees.
Tempest: bite me.
Hey folks, I’m just a passerby - I drifted this way while looking for mathematicians’ comments on this Wildberger’s trig revolution that has been reported on some online news feeds and such.
For what it’s worth, I’m one of those liberal arts majors held up as a straw man by tempest above, and I’m much too big a person to take it personally, so I won’t go into the atrocious grammar evinced by some mathematicians I know.
Anyway, I thought it might be useful to your discussion to point out that perhaps we’re missing the point about the usefulness of this new conceptual frame for trig.
What is the possibility of re-writing standard mathematical procedures in computer code without dealing with irrational numbers using this new system? Theoretically, it could lower both processing time and loss of precision. As a programming tool this could be more useful than simply as a way to teach the unwilling how to wrestle with triangles.
Just 2 cents’ worth from an incapable arts major.