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The three circumcircles through the triangle centroid G of a given triangle DeltaA_1A_2A_3 and the pairs of the vertices of the second Brocard triangle are called the McCay ...

In the mice problem, also called the beetle problem, n mice start at the corners of a regular n-gon of unit side length, each heading towards its closest neighboring mouse in ...

The Miquel point is the point of concurrence of the Miquel circles. It is therefore the radical center of these circles. Let the points defining the Miquel circles be ...

A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

A Moiré pattern is an interference pattern produced by overlaying similar but slightly offset templates. A simple example is obtained by taking two identical ruled ...

The Nagel line is the term proposed for the first time in this work for the line on which the incenter I, triangle centroid G, Spieker center Sp, and Nagel point Na lie. ...

The first Napoleon point N is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of the corresponding inner Napoleon ...

The Neuberg A_1-circle is the locus of the polygon vertex A_1 of a triangle on a given base A_2A_3 and with a given Brocard angle omega. From the center N_1, the base A_2A_3 ...

Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...