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New trigonometry is a sign of the time
physorg.com ^ | September 16, 2005

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


TOPICS: Business/Economy; Culture/Society; Front Page News; News/Current Events
KEYWORDS: ancient; astronomy; cosine; hindu; history; india; knowledge; math; matheducation; nasa; numbers; science; sine; space; trigonometry
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You can get rid of all the sines and cosines, etc., and replace them with "spread" and "quadrance," or "Jennifer" and "Pamela," and I still won't understand trigonometry.
1 posted on 09/18/2005 8:41:48 AM PDT by cloud8
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To: cloud8

I wonder when this will make it into my Calculus book...


2 posted on 09/18/2005 8:43:18 AM PDT by MikefromOhio (Hey Fox News, MORE MOLLY, LESS Greta van Talksoutthesideofhermouth)
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To: MikeinIraq; JimWforBush; The SISU kid

I wonder when this will make it into surveying equipment, if ever.

Civil Engineer Ping


3 posted on 09/18/2005 8:45:53 AM PDT by Fierce Allegiance
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To: cloud8

Though, might it be more fun if you did that?


4 posted on 09/18/2005 8:45:55 AM PDT by 1john2 3and4
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To: cloud8

Math is full of silly sounding words and funny looking symbols that put people off.


5 posted on 09/18/2005 8:47:43 AM PDT by Moonman62 (Federal creed: If it moves tax it. If it keeps moving regulate it. If it stops moving subsidize it)
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To: cloud8
How refreshing to be able to read new research in mathematics and actually understand what they are talking about.

The last article I tried to reed on Chaos Theory and Fractals made me cry.
6 posted on 09/18/2005 8:47:52 AM PDT by msnimje (Cogito Ergo Sum Republican)
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To: cloud8
I recall trig being the greatest and simplest math class I ever took. The teacher at the time was the keyboardist for Oingo Boingo (he bailed out before they became semi-famous).

He claimed to use trigonometric principles in his music (deciding which chords to play or something – don’t ask me).

That was all about a million years ago though. Like anything else, if you don’t use it for a couple of decades you may as well have never taken it.

7 posted on 09/18/2005 8:48:09 AM PDT by Who dat?
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To: MikeinIraq

> I wonder when this will make it into my Calculus book.

I was a victim of New Math, and have never fully recovered. Before that you had to (try to) memorize formulas. Maybe this trig system will right a thousand years of wrongs.


8 posted on 09/18/2005 8:49:30 AM PDT by cloud8
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To: MikeinIraq
"I wonder when this will make it into my Calculus book..."

If it’s a real improvement, maybe in a couple hundred years. Save your receipt.

9 posted on 09/18/2005 8:49:33 AM PDT by elfman2 (2 tacos short of a combination plate)
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To: cloud8
What's more, his simple new framework means calculations can be done without trigonometric tables or calculators, yet often with greater accuracy.

I'll believe that when I see it!

10 posted on 09/18/2005 8:51:28 AM PDT by Excuse_My_Bellicosity ( "Sic semper tyrannis." (Your dinosaur is ill.))
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To: Excuse_My_Bellicosity

How much accuracy does a high school trig student need?


11 posted on 09/18/2005 8:53:30 AM PDT by dr_who_2
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To: cloud8

Just the next step of DUMBING DOWN American students so we can fall to LAST PLACE in the world!

I still like clinton's head of the education dept having the parts of an animal cell reduced from (I am not a biologist) over 100 down to 4 stating - there is no need for anyone to learn any more than these basic four parts (it could have been six - been too many years). This is dangerous because he was speaking of COLLEGE LEVEL biology - where they teach medicine, bio-research, etc. It was a blatant dumbing-down measure.


12 posted on 09/18/2005 8:55:02 AM PDT by hombre_sincero (www.sigmaitsys.com)
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To: cloud8
From the promo on the book:

The book's content is largely elementary, but is presented concisely. It requires mathematical maturity and skill at algebraic manipulation, along with an interest in geometry and its applications. It will be especially valuable to
Professional mathematicians, especially those with an interest in geometry (including algebraic geometry and differential geometry), number theory, combinatorics and special functions
Scientists with an interest in mathematics, i.e. physicists, chemists
Engineers and some computer scientists
Mathematically talented high school students
Undergraduate mathematics or physics majors
High school and college mathematics teachers and lecturers
Amateur mathematicians with strong algebraic skills and an interest in geometry.
General members of the public who do not fit into one of these categories may well find the book too technical to be easily accessible. Dr Wildberger intends on writing a companion book at a more elementary level which explains the subject to the general public.

What simplification?
Smells fishy to me!
FReeeePeee!

13 posted on 09/18/2005 8:55:47 AM PDT by Leo Carpathian (FReeeePeee!)
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To: cloud8
His "simple" framework is anything but. By attempting to simplify high school trig, he's making college calculus and beyond exponentially harder. Take it from a guy with one year to go until he has a BS in EE, one in Math, and a BA in History (which really doesn't contribute much to the other two, but was fun. And we had actual girls in class. :D). I can explain further if anyone's interested, there was a long discussion about this on Slashdot.
14 posted on 09/18/2005 8:55:55 AM PDT by Lejes Rimul (Paleo and Proud)
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To: cloud8

OhMiGod, they killed Pricess SohCahToa!

Sine=Opposite/Hypotenuse

Cosine=Adjacent/Hypotenuse

Tangent=Opposite/Adjacent


15 posted on 09/18/2005 8:56:01 AM PDT by TruthShallSetYouFree (Abortion is to family planning what bankruptcy is to financial planning.)
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To: Moonman62

Math is essential exercise for a healthy brain and rational thought.


16 posted on 09/18/2005 8:59:14 AM PDT by montomike (Gay means happy and carefree...not an abomination against nature's check valve.)
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To: Who dat?
"The teacher at the time was the keyboardist for Oingo Boingo (he bailed out before they became semi-famous). "

No s~t? What’s his name? Where did he teach?

FWIW, I took a physics of music class that explained the relationship of musical intervals. Notes that are an an octave apart are twice the frequency, Fifths and thirds that compose a cord are roughly 150% and 133% apart in frequency and so on. We sense the harmony of that.

17 posted on 09/18/2005 8:59:27 AM PDT by elfman2 (2 tacos short of a combination plate)
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To: cloud8
New math was great (for those continuing in math and science).

Ever try casting out 9's?

18 posted on 09/18/2005 8:59:31 AM PDT by Paladin2 (MSM rioted over Katrina and looted the truth)
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To: Who dat?
I recall trig being the greatest and simplest math class I ever took.

I was going to say, what the heck's wrong with trig? I liked trig and found it perfectly clear.

The teacher at the time was the keyboardist for Oingo Boingo

That's hysterical.

19 posted on 09/18/2005 9:00:05 AM PDT by PianoMan (and now back to practicing)
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To: cloud8
Dr Norman Wildberger, has rewritten the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit.

From what I remember of trig, this was all trig was. The beginning stuff wasn't too difficult w/ a calculator.

If you got this concept, physics 101 was fairly easy to follow too.

20 posted on 09/18/2005 9:00:21 AM PDT by kstewskis ("I don't know what I know, but I know that it's big".....Jerry Fletcher)
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