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In mathematics, biangular coordinates are a coordinate system for the plane where ${\displaystyle C_{1}}$ and ${\displaystyle C_{2}}$ are two fixed points, and the position of a point P not on the line ${\displaystyle {\overline {C_{1}C_{2}}}}$ is determined by the angles ${\displaystyle \angle PC_{1}C_{2}}$ and ${\displaystyle \angle PC_{2}C_{1}.}$

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.

See also

• Two-center bipolar coordinates
• Bipolar coordinates
• Sectrix of Maclaurin

References

1. Naylor, Michael; Winkel, Brian (2010), "Biangular Coordinates Redux: Discovering a New Kind of Geometry", The College Mathematics Journal, 41 (1): 29–41
2. Ziatdinov, R.; Kim, T. W.; Nabiyev, R. I. (2015), "Two-point G1 Hermite interpolation in biangular coordinates", Journal of Computational and Applied Mathematics, 287: 1–11
3. Ziatdinov, R.; Yoshida, N.; Kim, T. W. (2017), "Visualization and analysis of regions of monotonic curvature for interpolating segments of extended sectrices of Maclaurin", Computer Aided Geometric Design, 56: 35–47

External links

• G. B. M. Zerr Biangular Coordinates, American Mathematical Monthly 17 (2), February 1910
• J. C. L. Fish, Coordinates Of Elementary Surveying
• George Shoobridge Carr, A synopsis of elementary results in pure mathematics (see page 742)

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