Skip to comments.New trigonometry is a sign of the time
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
I wonder when this will make it into my Calculus book...
I wonder when this will make it into surveying equipment, if ever.
Civil Engineer Ping
Though, might it be more fun if you did that?
Math is full of silly sounding words and funny looking symbols that put people off.
He claimed to use trigonometric principles in his music (deciding which chords to play or something dont ask me).
That was all about a million years ago though. Like anything else, if you dont use it for a couple of decades you may as well have never taken it.
> 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.
If its a real improvement, maybe in a couple hundred years. Save your receipt.
I'll believe that when I see it!
How much accuracy does a high school trig student need?
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.
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.
Smells fishy to me!
OhMiGod, they killed Pricess SohCahToa!
Math is essential exercise for a healthy brain and rational thought.
No s~t? Whats 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.
Ever try casting out 9's?
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
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.