Kite (geometry) across any one of its edges produces another tile; one of them is a right kite, with 60°, 90°, and 120° angles. The tiling that it produces by its reflections is the deltoidal trihexagonal tiling. Among all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter is an equidiagonal kite with angles π/3, 5π/12, 5π/6, 5π/12. Its four vertices lie at the three corners and one of the side midpoints of the Reuleaux triangle (above to the right). In non-Euclidean geometry, a Lambert quadrilateral is a right kite with three right angles. A quadrilateral is
Langley’s Adventitious Angles the first of the three unsolved problems listed by Rigby in his 1978 paper. Langley’s Adventitious Angles Langley’s Adventitious Angles is a mathematical problem posed by Edward Mann Langley in "The Mathematical Gazette" in 1922. In its original form the problem was as follows: formula_1 is an isosceles triangle. A solution was developed by James Mercer in 1923. This solution involves drawing one additional line, and then making repeated use of the fact that the internal angles of a triangle add up to 180° to prove that several triangles drawn within the large triangle are all isosceles. Many other solutions