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Let five circles with concyclic centers be drawn such that each intersects its neighbors in two points, with one of these intersections lying itself on the circle of centers. ...

Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter H. These circles cut the sides in six points lying on a ...

The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...

Three-dimensional generalization of the polyominoes to n dimensions. The number of polycubes N(n) composed of n cubes are 1, 1, 2, 8, 29, 166, 1023, ... (OEIS A000162; Ball ...

The radical circle of the McCay circles has center (1) which is not a Kimberling center, and radius (2) where (3) Its circle function is (4) where (5) which is also does not ...

An Aztec diamond of order n is the region obtained from four staircase shapes of height n by gluing them together along the straight edges. It can therefore be defined as the ...

The radical circle of the excircles has center at the Spieker center X_(10) and radius R_E=1/2sqrt((a^2b+ab^2+a^2c+abc+b^2c+ac^2+bc^2)/(a+b+c)). Its circle function is ...

The circumcircle of the Johnson triangle DeltaJ_AJ_BJ_C has center at the orthocenter H of the reference triangle and radius R, where R is the circumradius of the reference ...

The MacBeath circle, a term coined here for the first time, is the circumcircle of the MacBeath triangle. It has a fairly complicated radius, center function, and circle ...

Let DeltaA^'B^'C^' be the reflection of the orthic triangle of the reference triangle DeltaABC in the nine-point center. Then DeltaA^'B^'C^' and DeltaABC are in perspective, ...