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In geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the Mandart inellipse of a triangle
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, any three points, when non- colli ...
is an ellipse inscribed within the triangle, tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. Mo ...
to its sides at the contact points of its excircle
In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter.
...
s (which are also the vertices of the extouch triangle and the endpoints of the splitters
Splitter or splitters may refer to:
Technology
* DSL filter or DSL splitter, in telecommunications
* Fiber-optic splitter
* Hybrid coil, a three windings transformer
* Power dividers and directional couplers, in RF engineering
* Siamese connect ...
). The Mandart inellipse is named after H. Mandart, who studied it in two papers published in the late 19th century..;
. As cited by .
Parameters
As an inconic, the Mandart inellipse is described by theparameters
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
:
where ''a'', ''b'', and ''c'' are sides of the given triangle.
Related points
The center of the Mandart inellipse is the mittenpunkt of the triangle. The three lines connecting the triangle vertices to the opposite points of tangency all meet in a single point, theNagel point
In geometry, the Nagel point (named for Christian Heinrich von Nagel) is a triangle center, one of the points associated with a given triangle whose definition does not depend on the placement or scale of the triangle. It is the point of concurre ...
of the triangle.
See also
*Steiner inellipse
In geometry, the Steiner inellipse,Weisstein, E. "Steiner Inellipse" — From MathWorld, A Wolfram Web Resource, http://mathworld.wolfram.com/SteinerInellipse.html. midpoint inellipse, or midpoint ellipse of a triangle is the unique ellipse ins ...
, a different ellipse tangent to a triangle at the midpoints of its sides
Notes
External links
*{{mathworld, urlname=MandartInellipse, title=Mandart Inellipse Curves defined for a triangle