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A method of proof which proceeds by stating a proposition and then showing that it results in a contradiction, thus demonstrating the proposition to be false. In the words of ...

In three dimensions, there are three classes of constant curvature geometries. All are based on the first four of Euclid's postulates, but each uses its own version of the ...

Given a rectangle having sides in the ratio 1:phi, the golden ratio phi is defined such that partitioning the original rectangle into a square and new rectangle results in a ...

There are two common definitions of the trapezium. The American definition is a quadrilateral with no parallel sides; the British definition is a quadrilateral with two sides ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and ...

Smarandache sequences are any of a number of simply generated integer sequences resembling those considered in published works by Smarandache such as the consecutive number ...

Compass and straightedge geometric constructions dating back to Euclid were capable of inscribing regular polygons of 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, ...

The greatest common divisor, sometimes also called the highest common divisor (Hardy and Wright 1979, p. 20), of two positive integers a and b is the largest divisor common ...