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The area of the Steiner ellipse equals the area of the triangle times , and hence is 4 times the area of the Steiner inellipse. The Steiner ellipse has the least area of any ellipse circumscribed about the triangle. [1] The Steiner ellipse is the scaled Steiner inellipse (factor 2, center is the centroid). Hence both ellipses are similar (have ...
Example of an inellipse. In triangle geometry, an inellipse is an ellipse that touches the three sides of a triangle.The simplest example is the incircle.Further important inellipses are the Steiner inellipse, which touches the triangle at the midpoints of its sides, the Mandart inellipse and Brocard inellipse (see examples section).
c2) The Steiner inellipse of a triangle is the scaled Steiner Ellipse with scaling factor 1/2 and the centroid as center. Hence both ellipses have the same eccentricity , are similar . d) The area of the Steiner inellipse is π 3 3 {\displaystyle {\tfrac {\pi }{3{\sqrt {3}}}}} -times the area of the triangle.
Every triangle can be inscribed in an ellipse, called its Steiner circumellipse or simply its Steiner ellipse, whose center is the triangle's centroid. Every triangle has an infinitude of inscribed ellipses. One of them is a circle, and one of them is the Steiner inellipse which is tangent to the triangle at the midpoints of the sides.
Other examples are the Steiner ellipse, which is an ellipse passing through the vertices and having its centre at the centroid of the reference triangle; the Kiepert hyperbola which is a conic passing through the vertices, the centroid and the orthocentre of the reference triangle; and the Artzt parabolas, which are parabolas touching two ...
Other examples are the Steiner ellipse which is an ellipse passing through the vertices and having its centre at the centroid of the reference triangle, the Kiepert hyperbola which is a conic passing through the vertices, the centroid and the orthocentre of the reference triangle and the Artzt parabolas which are parabolas touching two ...
Marden's theorem states that the red dots are the foci of the ellipse. In mathematics , Marden's theorem , named after Morris Marden but proved about 100 years earlier by Jörg Siebeck, gives a geometric relationship between the zeroes of a third-degree polynomial with complex coefficients and the zeroes of its derivative .
Steiner point: the non-vertex point of intersection of the circumcircle with the Steiner ellipse.:: (The Steiner ellipse, with center = centroid (ABC), is the ellipse of least area that passes through A, B, C.