right|frame|Biangular coordinates
In mathematics, '''biangular coordinates''' are a coordinate system for the plane where <math>C_1</math> and <math>C_2</math> are two fixed points, and the position of a point ''P'' not on the line <math>\overline{C_1C_2}</math> is determined by the angles <math>\angle PC_1C_2</math> and <math>\angle PC_2C_1.</math><ref>{{Citation | last1 = Naylor | first1 = Michael | last2 = Winkel | first2 = Brian | title = Biangular Coordinates Redux: Discovering a New Kind of Geometry | journal = The College Mathematics Journal | volume = 41 | issue = 1 | pages = 29–41 | year = 2010 | doi = 10.4169/074683410X475092 | language = English}} </ref>
The sine rule can be used to convert from biangular coordinates to two-center bipolar coordinates.
==Applications== Biangular coordinates can be used in geometric modelling and CAD.<ref>{{Citation | last1 = Ziatdinov | first1 = R. | last2 = Kim | first2 = T. W. | last3 = Nabiyev | first3 = R. I. | title = Two-point G1 Hermite interpolation in biangular coordinates | journal = Journal of Computational and Applied Mathematics | volume = 287 | pages = 1–11 | year = 2015 | doi = 10.1016/j.cam.2015.02.040 | url = https://www.sciencedirect.com/science/article/pii/S0377042715001107 | language = English | url-access = subscription }}</ref><ref>{{Citation | last1 = Ziatdinov | first1 = R. | last2 = Yoshida | first2 = N. | last3 = Kim | first3 = T. W. | title = Visualization and analysis of regions of monotonic curvature for interpolating segments of extended sectrices of Maclaurin | journal = Computer Aided Geometric Design | volume = 56 | pages = 35–47 | year = 2017 | doi = 10.1016/j.cagd.2017.06.003 | url = https://www.sciencedirect.com/science/article/pii/S0167839617301206 | language = English | url-access = subscription }}</ref>
==See also== * Two-center bipolar coordinates * Bipolar coordinates * Sectrix of Maclaurin
==References== {{reflist}}
==External links== * [https://www.jstor.org/stable/2972096 G. B. M. Zerr Biangular Coordinates], ''American Mathematical Monthly'' 17 (2), February 1910 * [https://archive.org/details/coordinatesofele00fishrich/ J. C. L. Fish, ''Coordinates Of Elementary Surveying''] * [https://archive.org/details/synopsisofelemen00carrrich/page/742 George Shoobridge Carr, ''A synopsis of elementary results in pure mathematics''] (see page 742)
Category:Coordinate systems
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