biangular coordinates
Image:BiangularCoordinateSystem.JPG
In mathematics, biangular coordinates are a coordinate system for the plane where and are two fixed points, and the position of a point P not on the line is determined by the angles and {{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}}
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.{{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
| 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
}}
See also
References
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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)
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