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Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

The perspectrix X of a pair of paralogic triangles DeltaA_1A_2A_3 and DeltaB_1B_2B_3 bisects the line joining the two orthocenters H_A and H_B (Johnson 1929, p. 259).

The Tucker circles are a generalization of the cosine circle and first Lemoine circle which can be viewed as a family of circles obtained by parallel displacing sides of the ...

A lune is a plane figure bounded by two circular arcs of unequal radii, i.e., a crescent. (By contrast, a plane figure bounded by two circular arcs of equal radius is known ...

The three circular triangles A^'B^'C^', AB^'C^', A^'BC^', and A^'B^'C obtained by extending the arcs of a circular triangle ABC into complete circles.

Two triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 are orthologic if the perpendiculars from the vertices A_1, B_1, C_1 on the sides B_2C_2, A_2C_2, and A_2B_2 are concurrent. ...

A curve composed exclusively of circular arcs.

Pick a point O in the interior of a quadrilateral which is not a parallelogram. Join this point to each of the four vertices, then the locus of points O for which the sum of ...

One name for the figure used by Euclid to prove the Pythagorean theorem.

If isosceles triangles with apex angles 2kpi/n are erected on the sides of an arbitrary n-gon A_0, and if this process is repeated with the n-gon A_1 formed by the free ...