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
Sorry Bill Gates et al are my age and so probably had standard math instruction - geometry, algebra, trig, calc, def-eq, Linear algebra, and vectors and maybe numerical analysis. I had to take my daughter out of public school, because all they were teaching her was how to operate a calculator - they had a whole book on what buttons to push, no understanding, no reasoning. After just two years of classical instruction she is excelling at VA Tech.
If true, this is brilliant.
Posting to a guy that has a fully restored 1975 Kawasaki 900 sitting inside.....I understand you passion.
It's a joke (ha ha) to explain my overcompensation of now having a room full of computers at home.
If all one wants to do is find the reciprocal of a particular number, one can simply punch "1" "÷", then the number, then "=" and get the result. Not worth having a special button for that.
On the other hand, if one wants to compute the equivalent parallel resistance of a bunch of resistors, the reciprocal button makes it easy: [res1] "1/x" "+" [res2] "1/x" "+" [res3] "1/x" "=" "1/x". Doing such a computation without the reciprocal button would be rather nuisancesome.
BTW, until it got stolen, I had a Craig calculator with a fun little button called "EX". This would exchange the display register with the holding register. The fact that the calculator had "1/x" and "+/-" buttons obviated what would have been the primary need for this feature, but it was still cute. The calculator was also interesting in that it only had a single "M" key which could be used with other keys, not only for "MC", "M+", "M-", and "M=", but also for such fun things as "Mx" and "M÷" or the classic "M EX".
My second choice is a chromed out Harley Sportster.
Looks like "Math for dumb Liberals" - go get the $80 book put it on the shelf and be happy singing gumbayaaaaa!
>> I was a victim of New Math, and have never fully recovered.
> With all due respect, you were a victim of bad math teachers.
Screw the "due respect."
"Due respect" is for a bright kid who was stuck in a school in Arkansas.
My school and its teachers--math and otherwise--were superior to most. New math, however, was for kids with an aptitude for the subject. The *only* reason I wasted four years in AP math was for the ol' college record. My own intelligence and creativity lie elsewhere.
Obviously :)
Like "distance" and "angle" ? This guy wants to replace them with "quadrance" and "spread" - makes things simpler, he says.
As Howie Mandel says, "Mmmmmmmmmmmmmmmmmmm - no." His system is motivated by quite arcane considerations, and the only possible appeal that I can see is to its author. In his first chapter he mounts a polemic against angle and length measure, which requires a fair degree of sophistication to appreciate at all, especially since it's entirely wrongheaded.
Note that the two new fundamental concepts he introduces are identical to the square of the length of a line and the square of the sine of an angle, so all the clarity and ease he touts are obtainable by simply leaving these in squared form.
Criswell predicts this is going nowhere.
Using the basic trig formula sin(alpha+beta)= sin(45)=1/sqrt(2)
an exact answer can be obtained in about 6 short lines
without solving any messy equations
or using any of his pyrotechniques.
Interesting stuff. Please add me to the Civil Engineer ping list.
I've been meaning to find a copy of that book. I love the chapter dependency diagram at the beginning -- complicated to the point of being incomprehensible.
Give that man a cigar!
Sines and cosines have a life unto themselves -- you can't just define them out of existence. Pity the poor kid who learned "Divine Proportions" in high school, with no clue that he's about to get a very rude awakening in Freshman Calculus.
Inductance - Voltage leads current
Capacitance - Current leads voltage
Courtesy: US Naval Basic Electricity & Electronics Class "A" School
Great Lakes Naval Station, Ill. ('70)
(Jeez, 35 years, I remembered!)
How about:
Bad boys rape our young girls but violet gives willingly get some now...
It looks like 1978 or 79. It was before the Mystic Knights of Oingo Boingo was formed in 79 and their film Forbidden Zone in 1980, which was a follow up to that play.
Thats right. Also the theme song to Weird Science.
Hold on, we'll get 'round to that.
There are three kinds of people in the world. Those that understand math and those that don't. ;-)
Garde la Foi, mes amis! Nous nous sommes les sauveurs de la République! Maintenant et Toujours!
(Keep the Faith, my friends! We are the saviors of the Republic! Now and Forever!)
LonePalm, le Républicain du verre cassé (The Broken Glass Republican)
ROFLOL
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