Testwiki:Reference desk/Archives/Mathematics/2016 January 1

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January 1

What is the difference between Mathematics Q&A on Stack Exchange and Wikipedia Reference Desk

I'm doing a research project about free Q&A and I would like to know your opinion about these different if you have. Thank you 133.19.15.12 (talk) 08:16, 1 January 2016 (UTC)Yousef

Please see the notice at the top of this page: We don't answer requests for opinions, predictions or debate. Two obvious factual differences that come to mind are (1) the volume of questions on math.stackexchange.com is much higher than on the RefDesk; and (2) StackExchange has a formal system that lets users vote on the quality/accuracy of answers. AndrewWTaylor (talk) 10:42, 1 January 2016 (UTC)

You need to ask a mathematical question. Non-mathematical question should be asked on the Humanities page. 110.22.20.252 (talk) 12:19, 1 January 2016 (UTC)

If 'you are doing a research project' then it is your task to find and point out the differences. Do your homework yourself. --CiaPan (talk) 12:52, 3 January 2016 (UTC)

Jeez folks no need to bit off his head. Those responses will make an interesting data point though! Dmcq (talk) 14:56, 3 January 2016 (UTC)

Interpolating sine

Using the error expression of interpolation polynomial one obtains that we can approximate the function sin on the interval $[0,2^n]$ with an error bounded by $\approx \frac{1}{n!}$ using n points (in Chebyshev nodes).

My question is: With n points we get an interpolation polynomial of degree $\le n$, so it has up to n roots, but sine has $\approx 2^n$ roots in this interval. So, how could this come true? (or: How could we approximate it that well?) Notes:

1. The notation of "approximation" above should be understood as asymtotic notation.
2. The error expression could be found here: https://en.wikipedia.org/wiki/Chebyshev_nodes (the last expression)

213.8.204.34 (talk) 21:14, 1 January 2016 (UTC)

Check the error bound. There's a factor of ((b-a)/2)ⁿ which in this case would be 2^n(n-1). --RDBury (talk) 04:57, 2 January 2016 (UTC)

Oopss... My subtitution was wrong.. Thanx :) 213.8.204.22 (talk) 06:44, 2 January 2016 (UTC)