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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 decimal expansion of the reciprocal of the number seven, 1/7=0.142857142857...=0.142857^_, (1) which is a repeating decimal. Now take overlapping pairs of these ...

An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

The pedal circle with respect to a pedal point P of a triangle DeltaA_1A_2A_3 is the circumcircle of the pedal triangle DeltaP_1P_2P_3 with respect to P. Amazingly, the ...

Let a circle C_1 lie inside another circle C_2. From any point on C_2, draw a tangent to C_1 and extend it to C_2. From the point, draw another tangent, etc. For n tangents, ...

Triangle centers with triangle center functions of the form alpha=a^n are called nth power points. These points lie along the trilinear curve a^n:b^n:c^n that passes through ...

One of the three standard tori given by the parametric equations x = (c+acosv)cosu (1) y = (c+acosv)sinu (2) z = asinv (3) with c>a. This is the torus which is generally ...

The Sendov conjecture, proposed by Blagovest Sendov circa 1958, that for a polynomial f(z)=(z-r_1)(z-r_2)...(z-r_n) with n>=2 and each root r_k located inside the closed unit ...

The Stevanovic circle is a central circle with center X_(650), which has center function alpha_(650)=cosB-cosC, (1) It has radius (2) It has circle function ...