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# The death of sines, cosines, tangents

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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.

Basically, this shows how to simplify some calculations involving triangles by replacing angles and lengths with their respective squares. The downside is that some other calculations get more difficult, and that there is an abstraction cost to using the fairly unintuitive concepts of "quadrance" and "spread". As far as I can tell, he makes no attempt to replace sines in complex and Fourier analysis, for example.

Anyway, there isn't much new here. Mathematicians already know how to simplify formulas by cancelling out trigonometric functions and square roots by their inverses, and programmers who've tried to write efficient geometry code already know about these tricks as well.

This book might be an excellent reference for such tricks, and would be interesting to read, but the only "revolution" here is in the marketing.

i read this on slashdot. it makes me really happy because I cant stand trigonometry for that reason, SOHCAHTOA ugh I'm sick of it >_<

Well, the problem seems to be that in high school you define the trigonometric functions in terms of ratios between sides of triangles. The first thing I was taught about trigonometry in college was to forget that crap and define the functions in terms of the unit circle instead. Much easier, no mnemonics required, and the triangle definitions are trivial to derive when you need them.

thats good to know, but why do they teach it wrong all the time? I mean not just this, but back in first grade they said there were no negative numbers, even when I asked if there were because I heard about them. Then they say "forget that, there are". It makes no sense why they teach like that

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i hate math

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Aww, but Sine, Cosine and Tangent were one of the few things I was remotely good at in math around here. :P

Sines, cosines, tangents? What are these things you speak of?

To be honest I was expecting you guys (Fredrik at least) to be mourning.

Psyonisis said:

Math Sucks

Damn Straight.

insertwackynamehere said:

thats good to know, but why do they teach it wrong all the time? I mean not just this, but back in first grade they said there were no negative numbers, even when I asked if there were because I heard about them. Then they say "forget that, there are". It makes no sense why they teach like that

They don't teach it wrong, but you probably wouldn't understand the unit circle at a younger age as easily as you understand SOHCAHTOA. I learned the unit circle in precalc and it helped a lot.

DOOM Anomaly said:

Aww, but Sine, Cosine and Tangent were one of the few things I was remotely good at in math around here. :P

Same here, although I hated Trig.

Ralphis said:

They don't teach it wrong, but you probably wouldn't understand the unit circle at a younger age as easily as you understand SOHCAHTOA. I learned the unit circle in precalc and it helped a lot.

i'm in precalc now, hopefully we'll learn it this year

How can you draw a beautiful pentagram in a WAD without maths and trigonometry?

somewhere, there is a dead greek who gives a damn :p

This guy seems to be a bit off his rocker.

ducon said:

How can you draw a beautiful pentagram in a WAD without maths and trigonometry?

Indeed. From the authors' description of HR map29:

The pentagram was designed with precise calculations of sines and cosines to create a perfect pentagram, so please appreciate the effort.

Most subjects are simplified, or basically, you're taught a pack of lies, at pre-university and even at undergraduate level, because you wouldn't have a hope in hell of passing anything otherwise. it's one of those controversial things abotu education I debate about quite frequently. Some bits of Maths, and lots of biology, chemistry and physics are all basically lies at school. Take the old atom and electron thing you're taught at school. Essentially, it's wrong. The arts are also simplified so that quite often, opposites are in fact true when a highschool class discusses, for example, literary criticism.

The onus appears to be on how good a data retrieval system a child can be, and how much vague iffy knowledge they can assimalate, rather than actually educating them.

I hate math and don't give a damn.

As a game programmer, I can say that math sucks hairy horse cock. I want to write games, not turn into a math nerd. Thanks.

Programming and math more or less go hand in hand (depending slightly upon type of programming).

DooMBoy said:

I hate math and don't give a damn.

You hate maths or maths teachers? ;-)

He hates you, ducon! He hates you! ;-)

I love math and want Fredrik to teach me math

Kristian Ronge said:

Programming and math more or less go hand in hand (depending slightly upon type of programming).

Not really, in my experience. There is very little relation except that you sometimes want to perform mathematical calculations in programs.

As I said, it depends on the type of programming you're involved in. People have different experiences of it, as it's such a broad concept. For example, in the programming work I do (AI, Machine Learning at university) mathematics, mathematical statistics, mathematical logic and discrete mathematics are all essential.

Even outside of the academic world, there are numerous examples of when mathematics is important in programming. For instance, good luck coding a modern 3D engine without the use of mathematics.

Ok, this babysteps stuff is utter bullshit! You don't need baby steps. A child can learn ANYTHING that you cram in their little heads. ANYTHING! All you'd have to do is speak in algebraic equations and do them in front of them and they'd learn it. Because their brains are at a developmental state, where they will mimic anything around them to survive in their environment. That's why you simply need to talk to a child for them to learn to speak. And you can teach them 5 different languages (even more then that) and they'd still know it all with litte to no trouble. So screw baby steps dammit!

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