Diagonals

Diagonals The diagonals of Pascal's triangle contain the figurate numbers of simplices: * The diagonals going along the left and right edges contain only 1's.

In any convex quadrilateral the bimedians m, n and the diagonals p, q are related by the inequality : with equality holding if and only if the diagonals are equal.

Lengths of the diagonals The lengths of the diagonals in a convex quadrilateral ABCD can be calculated using the law of cosines on each triangle formed by one diagonal and two sides of the quadrilateral.

The most general kite has unequal diagonals, but there is an infinite number of (non-similar) kites in which the diagonals are equal in length (and the kites are not any other named quadrilateral).

The square’s diagonals are formed by two rows of same-sized mounds, some of which were excavated.

By deconstructing the show’s logo and using the four diagonals of the letter ‘’W’’ as a base grid for all on-air layouts, CapeRock gave the show a solid but unique foundation to build its visuals around.

A construction of a magic square of order 4 (This is reflection of Albrecht Dürer's square.) Go left to right through the square counting and filling in on the diagonals only.

Along the two diagonals are two Reuten, small triangular shovels with a slightly bent shaft.

Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length.

American Navajo Indians used bold diagonals and rectangular motifs.

An equivalent condition is that opposite sides are parallel (a square is a parallelogram), that the diagonals perpendicularly bisect each other, and are of equal length.

An equivalent condition is that the diagonals bisect each other and are equal in length.

An equivalent condition is that the diagonals perpendicularly bisect each other.

A sufficient condition for similarity of polygons is that corresponding sides and diagonals are proportional.

Composition IX has highly contrasted, powerful diagonals whose central form gives the impression of an embryo in the womb.

Concave quadrilaterals In a concave quadrilateral, one interior angle is bigger than 180° and one of the two diagonals lies outside the quadrilateral.

Different constraints Sometimes the rules for magic squares are relaxed, so that only the rows and columns but not necessarily the diagonals sum to the magic constant (this is usually called a semimagic square).

Equivalent conditions are that opposite sides are of equal length; that opposite angles are equal; or that the diagonals bisect each other.

If P is an interior point in a convex quadrilateral ABCD, then : From this inequality it follows that the point inside a quadrilateral that minimizes the sum of distances to the vertices is the intersection of the diagonals.

If the formats have approximately the same aspect ratios, the characteristic dimensions can be the format diagonals; if the aspect ratios differ considerably (e.