In geometry, the Steiner inellipse of a triangle is the unique ellipse inscribed in the triangle and tangent to the sides at their midpoints. It is an example of an inconic. By comparison the inscribed circle of a triangle is another inconic that is tangent to the sides, but not at the midpoints unless the triangle is equilateral. The Steiner inellipse is attributed by Dörrie to Jakob Steiner, and a proof of its uniqueness is given by Kalman.
The Steiner inellipse contrasts with the Steiner circumellipse, also called simply the Steiner ellipse, which is the unique ellipse that touches a given triangle at its vertices and whose center is the triangle's centroid.
Read more about Steiner Inellipse: Properties, Generalization
Famous quotes containing the word steiner:
“The variables are surprisingly few.... One can whip or be whipped; one can eat excrement or quaff urine; mouth and private part can be meet in this or that commerce. After which there is the gray of morning and the sour knowledge that things have remained fairly generally the same since man first met goat and woman.”
—George Steiner (b. 1929)