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The term "twisted sphere" is used to mean either a projective plane (Henle 1994, p. 110) or the corkscrew surface obtained by extending a sphere along a diameter and then ...

The vertex triangle of two distinct circumcevian triangles or circumanticevian triangles is perspective to the reference triangle. In addition, the vertex triangles of the ...

A triangle with side lengths a, b, and c and triangle area Delta satisfies a^2+b^2+c^2>=4sqrt(3)Delta. Equality holds iff the triangle is equilateral.

Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

The Brocard circle, also known as the seven-point circle, is the circle having the line segment connecting the circumcenter O and symmedian point K of a triangle DeltaABC as ...

The figure determined by four lines, no three of which are concurrent, and their six points of intersection (Johnson 1929, pp. 61-62). Note that this figure is different from ...

Graham's biggest little hexagon is the largest possible (not necessarily regular) convex hexagon with polygon diameter 1 (i.e., for which no two of the vertices are more than ...

An isosceles tetrahedron is a nonregular tetrahedron in which each pair of opposite polyhedron edges are equal, i.e., a^'=a, b^'=b, and c^'=c, so that all triangular faces ...

Keller conjectured that tiling an n-dimensional space with n-dimensional hypercubes of equal size yields an arrangement in which at least two hypercubes have an entire ...

The mean line segment length l^_ is the average length of a line segment in line segment picking within some given shape. As summarized in the following table (where Delta(3) ...