inellipses are the Steiner inellipse, which touches the triangle at the midpoints of its sides, the Mandart inellipse and Brocard inellipse (see examples section)...
14 KB (3,437 words) - 03:02, 12 June 2025
In geometry, the Steiner inellipse, midpoint inellipse, or midpoint ellipse of a triangle is the unique ellipse inscribed in the triangle and tangent...
11 KB (1,562 words) - 03:03, 12 June 2025
vertices z1, z2, z3 and tangent to the sides at their midpoints: the Steiner inellipse. The foci of that ellipse are the zeroes of the derivative p'(z). This...
9 KB (1,273 words) - 05:05, 24 April 2024
In geometry, the Mandart inellipse of a triangle is an ellipse that is inscribed within the triangle, tangent to its sides at the contact points of its...
3 KB (237 words) - 06:50, 11 October 2023
triangle and tangent to all three sides. Every triangle has a unique Steiner inellipse which is interior to the triangle and tangent at the midpoints of the...
55 KB (6,518 words) - 21:25, 19 June 2025
{\displaystyle c} remains constant. Every triangle has a unique Steiner inellipse – an ellipse inside the triangle and tangent to the midpoints of the three...
91 KB (12,021 words) - 17:33, 29 May 2025
called the Steiner circumellipse, to distinguish it from the Steiner inellipse. Named after Jakob Steiner, it is an example of a circumconic. By comparison...
10 KB (1,769 words) - 03:03, 12 June 2025
triangle, the inellipse with its center at that point is unique.: p.142 The inellipse with the largest area is the Steiner inellipse, also called the...
7 KB (1,398 words) - 02:26, 9 December 2022
(non-Euclidean geometry) Hypotenuse Incircle and excircles of a triangle Inellipse Integer triangle Isodynamic point Isogonal conjugate Isoperimetric point...
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vertices at the feet of the altitudes), and the only triangle whose Steiner inellipse is a circle (specifically, the incircle). The triangle of the largest...
25 KB (2,644 words) - 16:15, 29 May 2025
\triangle T_{A}T_{B}T_{C}} is called the Mandart circle (cf. Mandart inellipse). The three line segments A T A ¯ {\displaystyle {\overline {AT_{A}}}}...
34 KB (5,710 words) - 20:39, 2 April 2025
the roots of the derivative of the cubic are the foci of the Steiner inellipse of the triangle—the unique ellipse that is tangent to the triangle at...
68 KB (10,311 words) - 18:51, 6 July 2025
that are dual in this way include the Steiner ellipse and the Steiner inellipse, and the Kiepert hyperbola and the Kiepert parabola. In the following...
20 KB (1,630 words) - 12:07, 1 July 2025
the centroid, inellipses: ellipses which touch the sides of a triangle. Special cases are the Steiner inellipse and the Mandart inellipse. Ellipses appear...
90 KB (16,568 words) - 02:58, 12 June 2025
the Gergonne point. The mittenpunkt is also the centroid of the Mandart inellipse of the given triangle, the ellipse tangent to the triangle at its extouch...
4 KB (451 words) - 03:55, 15 November 2024
neighbored tangents coincide. This procedure results in a statement on inellipses of triangles. From a projective point of view the two triangles P 1 P...
4 KB (607 words) - 05:18, 22 July 2024
triangle. Every triangle has an inscribed ellipse, called its Steiner inellipse, that is internally tangent to the triangle at the midpoints of all its...
11 KB (1,415 words) - 06:32, 2 June 2025
the triangle with these points as its vertices has a unique Steiner inellipse that is tangent to the triangle's sides at their midpoints. The major...
10 KB (1,557 words) - 19:05, 1 July 2025
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. Every...
5 KB (650 words) - 05:38, 30 June 2025
orthic inconic that is tangent to the sides of the triangle △ABC is an inellipse and the orthic inconics of the other three possible triangles are hyperbolas...
13 KB (1,604 words) - 19:06, 22 January 2025
vertex of the extouch triangle and one of the points where the Mandart inellipse is tangent to the triangle side. The three splitters concur at the Nagel...
3 KB (294 words) - 20:09, 13 December 2022
S2CID 12307207. Scimemi, Benedetto, "Simple Relations Regarding the Steiner Inellipse of a Triangle", Forum Geometricorum 10, 2010: 55–77. An interactive applet...
18 KB (2,590 words) - 19:02, 22 January 2025
Poncelet–Steiner theorem Parallel axes rule Steiner–Lehmus theorem Steiner inellipse Steinerian Steiner point (computational geometry) Steiner point (triangle)...
9 KB (1,003 words) - 08:54, 18 February 2025
excircles of a triangle, as well as the triangle's inconics that are not inellipses, are externally tangent to one side and to the other two extended sides...
3 KB (347 words) - 17:21, 26 October 2024
point. This is shown in blue and labelled "N" in the diagram. The Mandart inellipse is tangent to the sides of the reference triangle at the three vertices...
3 KB (450 words) - 16:20, 28 May 2025
Marden's theorem states that the zeros of P' are the foci of the Steiner inellipse which is the unique ellipse tangent to the midpoints of the triangle formed...
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also made by August Leopold Crelle and Carl Gustav Jacob Jacobi. Mandart inellipse Trisected perimeter point Dussau, Xavier (April 2020). "Elementary construction...
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233, Lemma 1 A point in the interior of a triangle is the center of an inellipse of the triangle if and only if the point lies in the interior of the medial...
7 KB (878 words) - 17:23, 30 December 2024
Banach–Mazur compactum – Concept in functional analysis Ellipsoid method Steiner inellipse, the special case of the inner Löwner–John ellipsoid for a triangle. Fat...
7 KB (968 words) - 03:03, 14 February 2025