Geometry v. calculus
Dmitrii's calculus/analysis introduction of sine and cosine is interesting and definitely worth giving in this article. Yet, it seems to me that the standard geometric approach should be given as well, because CZ is an encyclopedia, where one expects to find world's standard knowledge presented as traditionally as possible. Therefore, unless I hear that there is strong disagreement, I will write a first introductory section with a few drawings illustrating the geometric definition and graphs of sine and cosine. Also the formula's for sin(α+β), and so on, are needed.
The definition of Pi (π), at the end of the article, is also interesting (and new to me), but would it not be better to move this to the article on Pi as one of the ways that Pi may be defined?--Paul Wormer 08:27, 1 November 2008 (UTC)
(This continues a discussion on my talk page, where I was wondering whether we should introduce vectors). I did a quick and dirty rewrite of the definition using Cartesian coordinates without using vectors:
I think that's a bit easier to understand. However, as Paul said, the article uses unit vectors in the proof of the sum formula, so I'll also have to think about how to do that part without vectors. Unfortunately, I ran out of time. So to be continued. Or, if you think the vector approach is better (and I agree with Paul that the difference is minimal and mostly semantics), please say so and I won't waste my time. -- Jitse Niesen 15:11, 13 November 2008 (UTC)
- When we decide to get rid of vectors, I can easily adapt the figures and replace arrow points by small dots indicating points in the plane (or something similar).--Paul Wormer 08:44, 14 November 2008 (UTC)