id: 05838889
dt: j
an: 2011a.00681
au: Winkel, Brian; Naylor, Michael
ti: Biangular coordinates redux: discovering a new kind of geometry.
so: Coll. Math. J. 41, No. 1, 29-41 (2010).
py: 2010
pu: Mathematical Association of America (MAA), Washington, D.C.
la: EN
cc: G50 G90
ut: coordinate systems
ci:
li: doi:10.4169/074683410X475092
ab: Summary: Biangular coordinates specify a point on the plane by two angles
giving the intersection of two rays emanating from two fixed poles.
This is a dual of Cartesian coordinates wherein a point on the plane is
described by two distances. Biangular coordinates, first written about
in 1803 in France, were subsequently studied in Britain at the end of
the 19th century. Contemporary students will enjoy plotting biangular
relations and discovering patterns in families of relations. The
mathematical shapes which are given by biangular relations include
standard shapes like lines, circles, hyperbolae and also unusual curves
like. Biangular coordinates elegantly describe some curves whose
representations are clumsy in other systems.
rv: