Wikipedia:Reference desk/Archives/Mathematics/2016 November 29
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November 29
editConstruction of higher roots of two
editCan or be constructed? יהודה שמחה ולדמן (talk) 17:28, 29 November 2016 (UTC)
![{\displaystyle {\sqrt[{4}]{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9aa163183b2c3828db27e22253d454a643a4c936)
![{\displaystyle {\sqrt[{2n}]{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3996f585ad5d2ec35a02e48be1efd22416b304ed)
- 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 and in general . But I believe you can't construct any other roots of 2. For example, is famously non-constructible, so can't be constructed either. -- Meni Rosenfeld (talk) 18:11, 29 November 2016 (UTC)
- So how do we construct as height in the right triangle with hypotenuse ? 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)
- So how do we construct as height in the right triangle with hypotenuse ? יהודה שמחה ולדמן (talk) 18:54, 29 November 2016 (UTC)
![{\displaystyle {\sqrt {2}},{\sqrt[{4}]{2}},{\sqrt[{8}]{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fdbc28582abeab2b5ba1031e96a0fdaf5816fa5c)
![{\displaystyle {\sqrt[{2^{n}}]{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ace0a957f888ba34fe897aaba5437023fd2140e9)
![{\displaystyle {\sqrt[{3}]{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9ca071ab504481c2bb76081aacb03f5519930710)
![{\displaystyle {\sqrt[{6}]{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2fd2e90711da1208f1bf08c8992ab44739cb9c57)
"Equivalent to" vs "Approximately" symbols
editWhat 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)