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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

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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

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)

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

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

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)

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)

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?

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

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)

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.))

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

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)

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!)

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)

To: cloud8

OhMiGod, they killed Pricess SohCahToa!

Sine=Opposite/Hypotenuse

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

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.)

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)

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)

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)

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)

To: cloud8
Thanks for the post.

I write trig functions in software for a living. This stuff might make some things faster, simply by avoiding trig functions.

You can do trig like stuff with matrix algebra, although I don't understand it except to use existing functions. It's much faster than trig functions. Maybe this stuff is based on a simplified matrix algebra.

21 posted on 09/18/2005 9:01:14 AM PDT by narby

To: TruthShallSetYouFree

It was CHIEF SohCahToa in my school....

God only knows how I passed trig, because I certainly don't!

Regards,

22 posted on 09/18/2005 9:04:51 AM PDT by VermiciousKnid

To: TruthShallSetYouFree

Oh, and we'd have been given a big, fat F if we'd be caught with a calculator. They weren't allowed even in class, nevermind at a test.

Regards,

23 posted on 09/18/2005 9:06:32 AM PDT by VermiciousKnid

To: cloud8

> These new concepts mean that trigonometric problems
> can be done with algebra ...

I've been doing a lot of angles work in constructing a
new house, and frankly, I'd rather work with classic
trig than algebra.

In any event, it will be interesting to see this theory.
Unfortunately, the wildegg site is pure hype, and the
web.maths.unsw.edu.au site is non-responsive.

24 posted on 09/18/2005 9:06:48 AM PDT by Boundless

To: Moonman62

Math is the most realistic, most wonderful and the only subject that keeps my brain engaged .

Social Science, literature, pottery, music etc are all crap compared to math. Math is awesome.

25 posted on 09/18/2005 9:10:37 AM PDT by velocityguy

To: TruthShallSetYouFree

SohCahToa got me through Trig and I passed on the info to my kid when he took Trig (somehow the teacher didn't mention it) and it got him through too, LOL.

Once you understand it's just ratios, it takes all the "mystery" out of it.

26 posted on 09/18/2005 9:10:43 AM PDT by dawn53

To: Excuse_My_Bellicosity

Yeah, I don't see how it could be done with greater accuracy. Trig is an exact science.

27 posted on 09/18/2005 9:11:48 AM PDT by Brilliant

To: Boundless
In any event, it will be interesting to see this theory. Unfortunately, the wildegg site is pure hype, and the web.maths.unsw.edu.au site is non-responsive.

The first chapter of the book is here.

28 posted on 09/18/2005 9:12:35 AM PDT by snowsislander

To: cloud8

maybe....

I was lucky enough to miss new math....

29 posted on 09/18/2005 9:12:40 AM PDT by MikefromOhio (Hey Fox News, MORE MOLLY, LESS Greta van Talksoutthesideofhermouth)

To: elfman2

LOL

ok

30 posted on 09/18/2005 9:12:53 AM PDT by MikefromOhio (Hey Fox News, MORE MOLLY, LESS Greta van Talksoutthesideofhermouth)

To: Doctor Stochastic

ping

31 posted on 09/18/2005 9:13:15 AM PDT by longshadow

To: Excuse_My_Bellicosity
I'll believe that when I see it!

Ditto!

32 posted on 09/18/2005 9:16:11 AM PDT by Publius6961 (Liberal level playing field: If the Islamics win we are their slaves..if we win they are our equals.)

To: cloud8

33 posted on 09/18/2005 9:16:25 AM PDT by CarrotAndStick (The articles posted by me needn't necessarily reflect my opinion.)

To: cloud8

""And we mathematicians wonder why so many people view our beautiful subject with distaste bordering on hostility."

Yep...still have bad memories of Mr. Bigalow for high school geometry trying to stuff my mathematically empty head with theoroms and postulates, etc.

However, when I got to college I had a wonderful woman professor who we called "Dr. Marie"...I had her for "Mathimatical Statistics" ...she was an outstanding instructor and her's was the only math class I took in all of my academic history that made any sense at all. (I got an "A") (Also learned a ton about playing "Keno" using statistics).

34 posted on 09/18/2005 9:17:17 AM PDT by Towed_Jumper

To: dr_who_2
How much accuracy does a high school trig student need?

To grasp the concept? Not much.
But I remember being an AA graduate in surveying and having a Structural engineer with a Masters join the company and doing a bunch of mapping calculations using pi as 3.14

Took me weeks to fix everything...

35 posted on 09/18/2005 9:19:02 AM PDT by Publius6961 (Liberal level playing field: If the Islamics win we are their slaves..if we win they are our equals.)

To: TruthShallSetYouFree

Wasn't that the volcanic island that blew up in the 1800's? ;)

Trig methods will still appeal more to the spatially-oriented than algebraic solutions.

36 posted on 09/18/2005 9:20:23 AM PDT by mikrofon ("Sine" of the X ?)

Ever try casting out 9's?

I remember that vaguely.
But I know for a fact that it wasn't until last year that I was exposed to a fascinating and useful concept: digital root!

37 posted on 09/18/2005 9:22:00 AM PDT by Publius6961 (Liberal level playing field: If the Islamics win we are their slaves..if we win they are our equals.)

To: Publius6961

Where did he graduate from?

38 posted on 09/18/2005 9:22:09 AM PDT by dr_who_2

To: cloud8

" we have relied on the false assumptions that distance is the best way to measure the separation of two points"

I didn't see any better assumption in his article. I googled up "quadrance" and "spread" and learned that that these are not linearly additive metrics. I suspect that this "new" trigonometry achieves simplicity by requiring complexity in the measurement of quadrance and spread. I can't think of anything simpler, or more intuitive, than using a ruler and a protractor.

Trig is elementary for folks with a bit of mathematical acuity. I really don't see the point of trying to devise a simpler trig. It's useless for most for those whose abilities are in other areas.

39 posted on 09/18/2005 9:22:32 AM PDT by RBroadfoot

To: TruthShallSetYouFree
How about those squaws?

There was this tribe of Indians in the old west who had a custom that whenever a couple was expecting, that the brave would venture into the wilderness, slay a mighty beast and bring the skin back to wrap the newborn in. It was supposed to bring the power and spirit of the slain animal to the new member of the tribe. Well, one particularly fertile year there were three couples expecting. The braves all went out into the wilderness about the same time to do their solemn duty to their newborn and to the tribe. The first brave went out and slew a grizzly bear and proudly returned with the skin to wrap his new baby boy in. The second brave went out and slew a cougar and proudly returned with the skin to wrap his new baby girl in. The third brave went to a special place he knew in the wilderness (there were those who suspected it was very close to the zoo), and slew a hippo, which he skinned. When he returned, he discovered that his wife had given birth to twins, a boy and a girl, which he proudly wrapped in the hippo skin.

This just goes to prove that age old adage (or is it a theorem?) Ready?

The squaw of the hippopatamus is equal to the sum of the squaws of the other two hides!

40 posted on 09/18/2005 9:23:04 AM PDT by raybbr

To: cloud8

I taught myself math, so I like it. But you have to spend a lot of time looking for the right books.

41 posted on 09/18/2005 9:23:16 AM PDT by Graymatter

To: montomike; velocityguy

I am a math major in case you two couldn't tell. Math is wonderful, but I think for most people it takes a really great teacher to get past the silly words and funny symbols.

42 posted on 09/18/2005 9:24:13 AM PDT by Moonman62 (Federal creed: If it moves tax it. If it keeps moving regulate it. If it stops moving subsidize it)

To: cloud8

oh great...now what do i do with all these x's & y's i've hoarding ?

43 posted on 09/18/2005 9:24:32 AM PDT by stylin19a (In golf, some are long, I'm "Lama Long")

To: Who dat?
Carl Graves teaches trig?
44 posted on 09/18/2005 9:24:54 AM PDT by elfman2 (2 tacos short of a combination plate)

To: cloud8

I did hear about a mathematician that got pi eyed.

45 posted on 09/18/2005 9:25:04 AM PDT by punster

To: cloud8
Take a look at Chapter 1 of the book. What I see is a complex replacement of sin/cos/tan with what amounts to the Pythagorean Theorem. You have to give up the concept of angle and distance and replace it with "quadrance" (distance squared) and "spread" (don't ask) and you still (obviously) have to be able to do square roots to get answers. So he makes you give up the intuitive idea of distance and angle just so you don't have to push the SIN, COS or TAN buttons on your calculator. Instead you have to push the SQR button several times.

This is progress?

46 posted on 09/18/2005 9:26:02 AM PDT by InterceptPoint

To: dr_who_2

UC

47 posted on 09/18/2005 9:28:04 AM PDT by Publius6961 (Liberal level playing field: If the Islamics win we are their slaves..if we win they are our equals.)

To: Graymatter
I taught myself math, so I like it. But you have to spend a lot of time looking for the right books.

Hogben...

48 posted on 09/18/2005 9:29:32 AM PDT by Publius6961 (Liberal level playing field: If the Islamics win we are their slaves..if we win they are our equals.)

To: cloud8
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

And yet he's left me still scratching my head since he failed to explain the five main rules.

49 posted on 09/18/2005 9:30:34 AM PDT by mtbopfuyn (Legality does not dictate morality... Lavin)

> New math was great (for those continuing in math and science).

SMSG math was utterly confusing.

> Ever try casting out 9's?

Check digits. That's not math...it's magic :)

50 posted on 09/18/2005 9:30:46 AM PDT by cloud8