 TOPICS  # Triangle Geometry

Triangle geometry is the study of the properties of triangles, including associated triangle centers, triangle lines, central circles, triangle cubics, and many others. These geometric objects often have remarkable properties with respect to the triangle.

An amazing number of connections between geometric structures occur in triangle geometry, prompting Crelle (1821) to state, "It is indeed a wonder that so simple a figure as the triangle is so inexhaustible in its properties," and J. Wetzel to remark that triangle geometry "has more miracles per square meter than any other area of mathematics" (Kimberling 1998, p. 1).

Triangle geometry lay dormant for most of the middle of the 20th century, but has recently arisen "from the dust and ashes that history has piled on it" (Davis 1995) by the use of computers to systematically study and geometric structures and their properties (Davis 1995, Kimberling 2005). In addition, experimental investigations using numeric approximations coupled with exact verification using computer algebra have resulted in remarkable productivity in triangle geometry (Kimberling 2005).

Circumconic, Inconic, Triangle, Triangle Center, Triangle Center Function, Triangle Cubic, Triangle Line, Trilinear Coordinates

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## References

Castellsaguer, Q. "The Triangles Web." http://www.xtec.es/~qcastell/ttw/ttweng/portada.html.Crelle, A. L. Sammlung mathematischer Aufsätze und Bemerkungen, Vol. 1. Berlin: Maurer, p. 176, 1821.Davis, P. J. "The Rise, Fall, and Possible Transfiguration of Triangle Geometry: A Mini-History." Amer. Math. Monthly 102, 204-214, 1995.Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Transfigured Triangle Geometry." Preprint. Mar. 5, 2005.

## Referenced on Wolfram|Alpha

Triangle Geometry

## Cite this as:

Weisstein, Eric W. "Triangle Geometry." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TriangleGeometry.html