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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. ...

By analogy with the outer Napoleon triangle, consider the external erection of three squares on the sides of a triangle DeltaABC. These centers form a triangle DeltaO_AO_BO_C ...

If A, B, and C are three points on one line, D, E, and F are three points on another line, and AE meets BD at X, AF meets CD at Y, and BF meets CE at Z, then the three points ...

The circle passing through the isodynamic points S and S^' and the triangle centroid G of a triangle DeltaA_1A_2A_3 (Kimberling 1998, pp. 227-228). The Parry circle has ...

A rectangle which cannot be built up of squares all of different sizes is called an imperfect rectangle. A rectangle which can be built up of squares all of different sizes ...

A perpendicular bisector CD of a line segment AB is a line segment perpendicular to AB and passing through the midpoint M of AB (left figure). The perpendicular bisector of a ...

A Pierpont prime is a prime number of the form p=2^k·3^l+1. The first few Pierpont primes are 2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433, 487, 577, 769, ... ...

A pivotal isogonal cubic is a self-isogonal cubic that possesses a pivot point, i.e., in which points P lying on the conic and their isogonal conjugates are collinear with a ...

Let a convex polygon be inscribed in a circle and divided into triangles from diagonals from one polygon vertex. The sum of the radii of the circles inscribed in these ...

Proportionally cutting circles are circles that intersect the sidelines of a reference triangle DeltaABC such that length of the chords that are cut off have lengths mua, ...