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The figure formed when the midpoints of the sides of a convex quadrilateral are joined in order is a parallelogram. Equivalently, the bimedians bisect each other. The area of ...

For a point P inside an equilateral triangle DeltaABC, the sum of the perpendiculars p_i from P to the sides of the triangle is equal to the altitude h. This result is simply ...

If each of two curves meets the line at infinity in distinct, nonsingular points, and if all their intersections are finite, then if to each common point there is attached a ...

A piecewise linear function is a function composed of some number of linear segments defined over an equal number of intervals, usually of equal size. For example, consider ...

A plane figure or solid compound consisting of multiple connected copies of a given base shape. For example, affixing n equal squares gives an n-polyomino, while affixing n ...

Somos defines a rational triangle as a triangle such that all three sides measured relative to each other are rational. Koblitz (1993) defined a congruent number as an ...

The upper irredundance number IR(G) of a graph G is the maximum size of an irredundant set of vertices in G. It is therefore equal to the size of a maximum irredundant set as ...

A parallelian is a line drawn parallel to one side of a triangle. The three lines drawn through a given point are known as the triangle's parallelians. There exists a unique ...

A Redheffer matrix is a square (0,1)-matrix with elements a_(ij) equal to 1 if j=1 or i|j (i divides j), and 0 otherwise. For n=1, 2, ..., the first few Redheffer matrices ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...