Search Results for ""

The outer Napoleon triangle is the triangle DeltaN_C^'N_B^'N_A^' formed by the centers of externally erected equilateral triangles DeltaABE_C^', DeltaACE_B^', and ...

The triangle bounded by the polars of the vertices of a triangle DeltaABC with respect to a conic is called its polar triangle. The following table summarizes polar triangles ...

Inscribe two triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 in a reference triangle DeltaABC such that A = ∠AB_1C_1=∠AC_2B_2 (1) B = ∠BC_1A_1=∠BA_2C_2 (2) C = ∠CA_1B_1=∠CB_2A_2. ...

The Spieker center is the center Sp of the Spieker circle, i.e., the incenter of the medial triangle of a reference triangle DeltaABC. It is also the center of the excircles ...

The Stammler circles are the three circles (apart from the circumcircle), that intercept the sidelines of a reference triangle DeltaABC in chords of lengths equal to the ...

The Steiner inellipse, also called the midpoint ellipse (Chakerian 1979), is an inellipse with inconic parameters x:y:z=a:b:c (1) giving equation ...

The tetrahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider a ...

Take any triangle with polygon vertices A, B, and C. Pick a point A_1 on the side opposite A, and draw a line parallel to BC. Upon reaching the side AC at B_1, draw the line ...

Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not explicitly derive equations for such surfaces. Beauville ...

Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...