In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, biangular coordinates are a
coordinate system
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...
for the
plane where
and
are two fixed points, and the position of a point ''P'' not on the
line is determined by the
angle
In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...
s
and
The
sine rule can be used to convert from biangular coordinates to
two-center bipolar coordinates
In mathematics, two-center bipolar coordinates is a coordinate system based on two coordinates which give distances from two fixed centers c_1 and c_2. This system is very useful in some scientific applications (e.g. calculating the electric field ...
.
Applications
Biangular coordinates can be used in geometric modelling and
CAD.
See also
*
Two-center bipolar coordinates
In mathematics, two-center bipolar coordinates is a coordinate system based on two coordinates which give distances from two fixed centers c_1 and c_2. This system is very useful in some scientific applications (e.g. calculating the electric field ...
*
Bipolar coordinates
*
Sectrix of Maclaurin
References
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)
Coordinate systems
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