- #1

bayan

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- Thread starter bayan
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- #1

bayan

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- #2

dduardo

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I just saw that. Here is a pdf explaining the technique:

http://web.maths.unsw.edu.au.nyud.net:8090/~norman/papers/Chapter1.pdf [Broken]

http://web.maths.unsw.edu.au.nyud.net:8090/~norman/papers/Chapter1.pdf [Broken]

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- #3

amcavoy

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- #4

Hurkyl

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First off, classical trigonometry (and length) has the huge advantages of being

Secondly, it touts as a "feature" that it treats corresponding angles identically. However, now the student is faced with multiple putative solutions (possibly a great many) from which 'e must distill the desired solution.

Finally, we already have well-understood tools for doing coordinate geometry: the dot and cross products. They do at least the same thing, but have the huge, giant, overwhelming advantage of being

- #5

Just skimming the pdf, his "quadrance" is in no way different from "length"; and his "spread" is the 'ratio of quadrances' - i.e., the cosine, or the normalized scalar product. And there are many basic algebraic errors throughout! :grumpy:

"spread" = cosine

- #6

arildno

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Has he never heard of an unmarked ruler??

Just because analytic geometry will use square roots in order to express distances in terms of Cartesian coordinates, does not in any way change the fact that "length" or "distance" arguably remains (one of) the most fundamental concepts in geometry.

- #7

amcavoy

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[itex]\sin^2{\left(45^o\right)}=\frac{1}{4}[/itex]

[itex]\sin^2{\left(60^o\right)}=\frac{3}{4}[/itex]

I don't see why this is new.

- #8

LeonhardEuler

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