complete quadrangle

It was set around a complete quadrangle, and built of rusticated stone.

Based on four points, the complete quadrangle has pairs of opposite sides and diagonals.

Complete quadrangle (projective geometry), a configuration with four points and six lines.

The projective dual of a complete quadrangle is a complete quadrilateral, and vice versa.

The six lines of a complete quadrangle meet in pairs to form three additional points called the diagonal points of the quadrangle.

To see the complete quadrangle applied to obtaining the midpoint, consider the following passage from J. W. Young:

Another approach to the harmonic conjugate is through the concept of a complete quadrangle such as KLMN in the above diagram.

The complete quadrangle was called a tetrastigm by , and the complete quadrilateral was called a tetragram; those terms are occasionally still used.

The three pairs of opposite sides of a complete quadrangle meet any line (not through a vertex) in three pairs of an involution.

For any two complete quadrangles, or any two complete quadrilaterals, there is a unique projective transformation taking one of the two configurations into the other.

Furthermore, this book (page 43) uses the complete quadrangle to "construct the fourth harmonic associated with three points on a straight line", the projective harmonic conjugate.

Jones succeeds in showing how Pappus manipulated the complete quadrangle, used the relation of projective harmonic conjugates, and displayed an awareness of cross-ratios of points and lines.

In his Geometrie der Lage Staudt introduced a harmonic quadruple of elements independently of the concept of the cross ratio following a purely projective route, using a complete quadrangle or quadrilateral.

In mathematics, specifically projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting each pair of points.

Due to the discovery of the Fano plane, a finite geometry in which the diagonal points of a complete quadrangle are collinear, some authors have augmented the axioms of projective geometry with Fano's axiom that the diagonal points are not collinear, while others have been less restrictive.

The college then had a complete quadrangle of buildings, save for a gap between the chapel and the hall that would later be filled by the principal's lodgings, built by Thelwall at his own expense; the library (later demolished) was outside the quadrangle, to the west of the north end of the lodgings.