De Longchamps point
Encyclopedia
In geometry
, the de Longchamps point of a triangle
is the reflection
of its orthocenter about its circumcenter. It is listed as X(20) in the Encyclopedia of Triangle Centers
. Its trilinear coordinates
are
The point is collinear
with the orthocenter and circumcenter.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the de Longchamps point of a triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
is the reflection
Reflection (mathematics)
In mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as set of fixed points; this set is called the axis or plane of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection...
of its orthocenter about its circumcenter. It is listed as X(20) in the Encyclopedia of Triangle Centers
Encyclopedia of Triangle Centers
The Encyclopedia of Triangle Centers is an on-line list of more than 3,000 points or "centers" associated with the geometry of a triangle. It is maintained by Clark Kimberling, Professor of Mathematics at the University of Evansville....
. Its trilinear coordinates
Trilinear coordinates
In geometry, the trilinear coordinates of a point relative to a given triangle describe the relative distances from the three sides of the triangle. Trilinear coordinates are an example of homogeneous coordinates...
are
The point is collinear
Line (geometry)
The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...
with the orthocenter and circumcenter.