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Consider the general system of two first-order ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y). (2) Let x_0 and y_0 denote fixed points with x^.=y^.=0, so ...

The points of tangency of the Lucas inner circle with the Lucas circles are the inverses of the vertices A, B, and C in the Lucas circles radical circle. These form the Lucas ...

The Lucas tangents triangle (a term coined here for the first time) is the triangle DeltaT_AT_BT_C formed by the pairwise tangents of the Lucas circles of a given reference ...

The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...

A random closed set (RACS) in R^d is a measurable function from a probability space (Omega,A,P) into (F,Sigma) where F is the collection of all closed subsets of R^d and ...

Triangle picking is the process of picking triangles at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a random ...

Let three isoscelizers I_(AC)I_(AB), I_(BA)I_(BC), and I_(CA)I_(CB) be constructed on a triangle DeltaABC, one for each side. This makes all of the inner triangles similar to ...

The unique (modulo rotations) scalene triangle formed from three vertices of a regular heptagon, having vertex angles pi/7, 2pi/7, and 4pi/7. There are a number of amazing ...

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, ...

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric ...