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
When I was a junior in high school, Mr. Carlson had all boys in his class, so he taught us this way:
Sally Can Tell
Oscar Has
A Hard
On Always
That's unforgettable. He also showed us the first electronic calculator we had ever seen. He rolled it in on a wheeled table. It was about 2 feet by 2 feet and used nixie tubes to display the result.
***Ever try casting out 9's?***
Oh, heck, we did casting out nines in highschool math in the 1940s. I learned to do it, but I've always wondered what good it did. I add by tens instead. Care to explain?
Casting out 9's ? I thought that was in only double-deck Canasta ?
Not really, just a trollish comment to see if anyone else remembered casting out as a check for errors.
Nixie tubes are so cool looking.
I have bad memories of college freshman Algebra. The prof would chicken scratch the first few variables on the board, get sidetracked, and leave us to wonder what the heck came next. Students, young and old, were dropping the class like flies. Those who didn't bail out before the cut off date merely signed their names to the final and turned it in blank. Two things got me through the course with a B: 1) I'd already complained to the head of the department and 2) I was dating the prof's pet who was a math whiz.
Ok, so what's a digital root?
replace web. with www.
> Then why does casting out 7's work in octal (base 8 for those who took new math)?
I knew this was a trick question!!!
Sixes in base 7?
No, Joe Berland.
The only tune I knew by Oingo Boingo was one that ended up on the Fast Times at Ridgemont High soundtrack in the 80’s (“Goodbye, goodbye” or something like that) .
Everyone always asked him about that, but he indicated that he had left the band years before they became “famous” (if you could call it that). Evidently they had been around for a long time before they ended up on that soundtrack.
"Social Science, literature, pottery, music etc are all crap compared to math. Math is awesome."
I have to completely agree with you. I have no doubt the Bard's pottery fell well short of his poetry and prose.
SMSG made prefect sense and allowed me to sit in the back of the class reading Heinlein and biographies of U.S. Frontier Explorers.
***Not really, just a trollish comment to see if anyone else remembered casting out as a check for errors.***
LOL! Thanks.
Trigonometry was easy, especially compared to calculus. I see no reason or purpose in making it even easier.
F's in hex.
Rational trigonometry makes it all much simpler, by replacing transcendental functions like cos, sin and tan with arithmetic and high school algebra.
I learned trig in the 8th and 9th grade using basic arithmetic and high school algebra. Tangent = opposite length/adjacent length, Cosine = opposite length / hypotenuse length. I don't know how you can get simpler than that.
For sines, cosines, and tangents of angles, a $10 calculator eliminates look-up tables, gives you trig values for any odd angle you can punch in there (so that you don't have to use linear interpolation for angles like 28.7893 degrees), and they generally give you results better than 6 decimal places. How is this guy's results more accurate than that?
I also noticed that when you Google this guy, you get nothing but the link to his book at wildegg.com. If this guy is a brilliant mathematician who is rewriting Euclidian mathematics and devising systems better than Newtonian coordinate systems, why doesn't he have write-ups in publications like Scientific American and mathematical periodicals? This whole thing is looking more and more like a money-making gimmick to me. I would think engineering firms would be beating this guy's door down if he were for real.
"Sined...Seeled...Delivered"
Very much agreed. In fact, we studied it independently and taught it to ourselves. I got a hundred in almost every test.
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