Wikipedia:Reference desk/Archives/Mathematics/2016 November 29

= November 29 =

Construction of higher roots of two
Can $$\sqrt[4]2$$ or $$\sqrt[2n]2$$ be constructed? יהודה שמחה ולדמן (talk) 17:28, 29 November 2016 (UTC)
 * You can always construct the geometric mean of two given lengths. Which means that if you are given a unit interval, you can construct the square root of any given number. This means you can construct $$\sqrt{2}, \sqrt[4]2, \sqrt[8]2$$ and in general $$\sqrt[2^n]2$$. But I believe you can't construct any other roots of 2. For example, $$\sqrt[3]2$$ is famously non-constructible, so $$\sqrt[6]{2}$$ can't be constructed either. -- Meni Rosenfeld (talk) 18:11, 29 November 2016 (UTC)
 * So how do we construct $$\sqrt[4]2$$ as height in the right triangle with hypotenuse $$1+\sqrt2$$ ? יהודה שמחה ולדמן (talk) 18:54, 29 November 2016 (UTC)
 * You can see the details of the construction at http://math.stackexchange.com/a/708/153429. -- Meni Rosenfeld (talk) 19:35, 29 November 2016 (UTC)

"Equivalent to" vs "Approximately" symbols
What is the difference between these symbols: ≍ ≈ ? I've seen "≈" used many times before (i.e. Pi ≈ 3.14). But "≍" is new to me. It seems they have a similar meaning? --209.203.125.162 (talk) 21:06, 29 November 2016 (UTC)


 * The ≍ symbol is sometimes used to denote equivalent "order of magnitude" in asymptotic analysis, for example, in Asymptotic notations. --Mark viking (talk) 21:49, 29 November 2016 (UTC)