User talk:Karl Stroetmann

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Hello, Karl Stroetmann, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers:

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Hello

I've seen your important contributions for the article Recurrence relation. I'm looking for the general (non-iterative) algebraic expression for the exact trigonometric constants of the form: ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$, when n is natural (and is not given in advance). Do you know of any such general (non-iterative) algebraic (non-trigonometric) expression?

• Let me explain: if we choose n=1 then the term ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$ becomes "0", which is a simple (non-trigonometric) constant. If we choose n=2 then the term ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$ becomes ${\begin{aligned}{\frac {1}{\sqrt {2}}}\end{aligned}}$, which is again an algebraic (non-trigonometric) constant. etc. etc. Generally, for every natural n, the term ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$ becomes an algebraic (non-trigonometric) constant. However, when n is not given in advance, then the very expression ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$ per se - is not an algebraic expression but rather is a trigonometric (non-algebraic) expression. I'm looking for the general (non-iterative) algebraic (non-trigonometric) expression equivalent to ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$, when n is not given in advance. If not for the cosine - then for the sine or the tangent or the cotangent.

Eliko (talk) 08:26, 31 March 2008 (UTC)