$kite geometry$

Equivalently, it is a quadrilateral whose four sides can be grouped into two pairs of adjacent equal-length sides. Kites also form the faces of several face-symmetric polyhedra and tessellations, and have been studied in connection with outer billiards, a problem in the advanced mathematics of dynamical systems.Ī kite is a quadrilateral with reflection symmetry across one of its diagonals. Kites of two shapes (one convex and one non-convex) form the prototiles of one of the forms of the Penrose tiling. The quadrilateral with the greatest ratio of perimeter to diameter is a kite, with 60°, 75°, and 150° angles. They include as special cases the right kites, with two opposite right angles the rhombi, with two diagonal axes of symmetry and the squares, which are also special cases of both right kites and rhombi. The convex kites are exactly the quadrilaterals that are both orthodiagonal and tangential.

Įvery kite is an orthodiagonal quadrilateral (its diagonals are at right angles) and, when convex, a tangential quadrilateral (its sides are tangent to an inscribed circle). A kite may also be called a dart, particularly if it is not convex. Kites are also known as deltoids, but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals. Kite quadrilaterals are named for the wind-blown, flying kites, which often have this shape and which are in turn named for a hovering bird and the sound it makes. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. A kite, showing its pairs of equal length sides and its inscribed circle.

Kite geometry