So9
I hated Trig. Still do. In the 35+ years since I took Trig in high school and later college (3 times to get a "C") I have never once had any use whatsoever for what I learned. To me there's no logic or flow to Trig as it was taught to me. Maybe there is but no one ever made that clear at all.
And I have Math ability. I took Calculus 1 and got a B so I know it's not me. I sat my son down after he graduated from public school after he did horribly in Math on his SAT test and made a 19 on his first college test in a basic "refresher" (non-credit) course. I taught him how doing algebra was just like working a puzzle and how simple it can be by just figuring out the puzzle based on what you already know. This semester he's now taking Differential Equations and Calculus Based Physics. Again, someone can have the ability, but its all how its taught that determines how well someone does in Math.
But I still wouldn't know a sine from a cosine if they bit me in the butt. I do know what a tangent is. That's about it.
Some Old Hags
Cackle All Hours
Till Old Age
Sine = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
It appears to be a press release to sell a book. I'd like to see this "new" method before I decide to apply it (if that's even possible).
e^(i*x) = cos(x)+ i*sin(x); % Euler's Rule
where i == sqrt(-1)
Complex exponentials are the eigen (characteristic) functions of linear systems. They can have my complex exponentials when they pry them from by cold calmy calculator.
Crap, now I'm gonna have to replace my sliderule.
Darn! I kind of liked Geometry and Trig.
OK. I've got a doctorate in math, and do research in geometry, and have looked at this stuff, and I've figured out what this guy is trying to accomplish.
It's a good idea.
It is NOT a good idea to teach INSTEAD of the standard geometry trigonometry, as long as all the rest of mathematics uses the standard functions. However, it IS a good way to teach the subjects of geometry and trigonometry themselves, as long as, at some point inthe course, the STANDARD definitons are introduced and their basic properties are proved.
Basically, the "quadrance" of a line segment is the square of its standard length, and the "spread" of an angle is the square of the sine of the angle. If you make these your fundamental quantities, most formulas and computations become simpler and their logical foundations become clearer. As long as, by the end of the course, students can translate freely between the two ways of looking at things, no harm is done, and a lot of conceptual and computational obstacles are avoided.
Almost every problem in standard trigonometry which requires a numerical solution must be solved by calculators or tables with messy approximations, even though the ultimate answer can be expressed in terms of the initial data by rational operations and square roots (and square roots are much, much, easier to calculate "by hand" than sines, cosines, and tangents). So Wildberger is onto something, though he's up against millennia of pedagogic tradition.
If true, this is brilliant.
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)
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