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The radical circle of the Lucas circles is the circumcircle of the Lucas tangents triangle. Its center has trilinear center function alpha_(1151)=2cosA+sinA (1) corresponding ...

The Moses-Longuet-Higgins circle is the radical circle of the circles centered at the vertices A, B, and C of a reference triangle with respective radii b+c-a, c+a-b, and ...

The tangential mid-arc circle is the circumcircle of the tangential mid-arc triangle. Its center and radius appear to be very complicated functions. Its center is not in ...

Prince Rupert's cube is the largest cube that can be made to pass through a given cube. In other words, the cube having a side length equal to the side length of the largest ...

The second blackboard problem in the 1997 film Good Will Hunting asks for all the series-reduced trees (referred to by the alternate term "homeomorphically irreducible trees" ...

Tutte's fragment (Taylor 1997) is the 15-node graph illustrated above (Grünbaum 2003, pp. 358-359 and Fig. 17.1.3). If the graph obtained by adding pendant edges to corners ...

An equichordal point is a point p for which all the chords of a curve C passing through p are of the same length. In other words, p is an equichordal point if, for every ...

For a triangle DeltaABC and three points A^', B^', and C^', one on each of its sides, the three Miquel circles are the circles passing through each polygon vertex and its ...

The locus of the point at which two given circles possess the same circle power is a straight line perpendicular to the line joining the midpoints of the circle and is known ...

The surface of revolution generated by the external catenary between a fixed point a and its conjugate on the envelope of the catenary through the fixed point is equal in ...