Colunar triangle
←Created page with '{{Geometry-stub}} In spherical geometry, '''colunar triangles''' are spherical triangles which have one side in common and whose other sides belong to the same great circles.{{cite book |last=Casey |first=John |date=1889 |title=A Treatise on Spherical Trigonometry, and Its Application to Geodesy and Astronomy|url=https://archive.org/details/atreatiseonsphe00casegoog/page/9/mode/2up |location=Dublin |publisher=Hodges, Figgis, a...' New page
In [[spherical geometry]], '''colunar triangles''' are [[spherical triangles]] which have one side in common and whose other sides belong to the same [[Great circle|great circles]].{{cite book |last=Casey |first=John |date=1889 |title=A Treatise on Spherical Trigonometry, and Its Application to Geodesy and Astronomy|url=https://archive.org/details/atreatiseonsphe00casegoog/page/9/mode/2up |location=Dublin |publisher=Hodges, Figgis, and Co. |page=10}}
A spherical triangle has three colunar triangles. Each one is created by replacing one of the vertices of the spherical triangle with its [[antipodal point]] (i.e. the point on the sphere which is diametrically opposite it). Together, a spherical triangle and one of its colunar triangles make up a [[spherical lune]].
Modern treatments of the subject restrict the definition to colunar triangles to spherical triangles of a particular type, namely [[Schwarz triangles]].[https://mathworld.wolfram.com/ColunarTriangle.html Weisstein, Eric W. "Colunar Triangle." From MathWorld--A Wolfram Resource.
