This topic was posted , thanks cloud8.
Posted on 09/18/2005 8:41:47 AM PDT by cloud8
Mathematics students have cause to celebrate. A University of New South Wales academic, Dr Norman Wildberger, has rewritten the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit.
What's more, his simple new framework means calculations can be done without trigonometric tables or calculators, yet often with greater accuracy.
Established by the ancient Greeks and Romans, trigonometry is used in surveying, navigation, engineering, construction and the sciences to calculate the relationships between the sides and vertices of triangles.
"Generations of students have struggled with classical trigonometry because the framework is wrong," says Wildberger, whose book is titled Divine Proportions: Rational Trigonometry to Universal Geometry (Wild Egg books).
Dr Wildberger has replaced traditional ideas of angles and distance with new concepts called "spread" and "quadrance".
These new concepts mean that trigonometric problems can be done with algebra," says Wildberger, an associate professor of mathematics at UNSW.
"Rational trigonometry replaces sines, cosines, tangents and a host of other trigonometric functions with elementary arithmetic."
"For the past two thousand years we have relied on the false assumptions that distance is the best way to measure the separation of two points, and that angle is the best way to measure the separation of two lines.
"So teachers have resigned themselves to teaching students about circles and pi and complicated trigonometric functions that relate circular arc lengths to x and y projections – all in order to analyse triangles. No wonder students are left scratching their heads," he says.
"But with no alternative to the classical framework, each year millions of students memorise the formulas, pass or fail the tests, and then promptly forget the unpleasant experience.
"And we mathematicians wonder why so many people view our beautiful subject with distaste bordering on hostility.
"Now there is a better way. Once you learn the five main rules of rational trigonometry and how to simply apply them, you realise that classical trigonometry represents a misunderstanding of geometry."
Wild Egg books: http://wildegg.com/ Divine Proportions: web.maths.unsw.edu.au/~norman/book.htm
Source: University of New South Wales
math ping
LOL!
Trust me -- the "trig crap" is invaluable in the real world. (At least, in my real world....)
hehe I know...
when I was an FO in the Army, we used RT factors all the time. Which was Trigonometry in a simple form.
Fun stuff. I barely remember it hehe :)
Right, but in standard geometry the basic unit is the angle, not the cosine of the angle, and there is no way to go numerically between the two without a calculator or tables. This reformulation avoids having any angle variable in any formula, so you can always calculate the answer in terms of the initial data without having to use calculators or tables and without the inevitable inexactness that results.
(You may end up at the end with some square roots, but they are very easy to calculate by hand to many decimal places, unlike sines and cosines.)
Could you list the "right" books. I am always looking for good books. I dabble in math study and would love to find something that could actually re-teach me math.
Most of the books I learned from are at least forty years out of print. There was a Modern Algebra Book One, and a Book Two just as good, one of the authors was Dolciani, but later editions or works by Dolciani I can't recommend---and the Geometry in the same series was crappe.
My favorite math book was written in the 1920's, my grandfather passed it on to me.
Ooh! There was the four-part World of Mathematics, sort of a math encylopedia. Not something that you read cover-to-cover, but it certainly helped relate math to the rest of human life! :) It was printed in the 1950's.
Also "The Mathematical Experience" by Phil Davis and Reuben Hersh was great.
My kid uses several math books, around an 8th-10th grade level. Heath Mathematics is excellent, authors Rucker, Dilley and Lowry, c 1987. And Pre-Algebra Mathematics by Gerald S. Lieblich, c 1973 by Bell and Howell. Great book, but none of the pretty pics you find in more recent works. Heath Mathematics is more colorful and touchy-feely.
And, in my opinion, math students should learn how to use an abacus and a slide rule. Also, nowadays hardly any math books give due attention to computation of degrees-minutes-seconds. For that matter, they give too little attention to computation in general. Math is like music, you have to practice.
And like with music, it is only an ordeal if you're practicing near an unappreciative audience. If you have a teacher who finds math fascinating, you will find math fascinating.
I had no teachers. But it would have been nice. My kids take learning like they were being handed precious gems, because that's the spirit in which I convey it, but I was a lone prospector in my time. :)
Joe Berland was my math teacher at Newbridge in Los Angeles and in fact he told me that he was the keyboardist for the MNOB... I am not sure but it kind of looks like him on the gong show at the very start...
Forget the receipt, you better sell now...
6 significant digits
I laughed everytime someone said they took some “new math” teaching style. Because the second they take a REAL math course in college, and it doesn’t matter if it bonehead Math 91 (intro),the Prof or TA would drag them back to the tried and true methods developed throughout math history...
Joe Berland was my math teacher at Newbridge in Los Angeles and in fact he told me that he was the keyboardist for the MNOB... I am not sure but it kind of looks like him on the gong show at the very start...
This topic was posted , thanks cloud8.
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