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In Euclidean geometry, an equidiagonal quadrilateral is a convex quadrilateral whose two diagonals have equal length. Equidiagonal quadrilaterals were important in ancient Indian mathematics , where quadrilaterals were classified first according to whether they were equidiagonal and then into more specialized types.
Strange matter: A type of quark matter that may exist inside some neutron stars close to the Tolman–Oppenheimer–Volkoff limit (approximately 2–3 solar masses). May be stable at lower energy states once formed. Quark matter: Hypothetical phases of matter whose degrees of freedom include quarks and gluons Color-glass condensate
When an equidiagonal kite has side lengths less than or equal to its diagonals, like this one or the square, it is one of the quadrilaterals with the greatest ratio of area to diameter. [ 21 ] A kite with three 108° angles and one 36° angle forms the convex hull of the lute of Pythagoras , a fractal made of nested pentagrams . [ 22 ]
Equidiagonal quadrilateral; Ex-tangential quadrilateral; G. Golden rectangle; Golden rhombus; H. ... This page was last edited on 3 November 2020, at 13:20 (UTC).
In elementary geometry, a quadrilateral whose diagonals are perpendicular and of equal length has been called a midsquare quadrilateral (referring to the square formed by its four edge midpoints). [ 1 ] [ 2 ] These shapes are, by definition, simultaneously equidiagonal quadrilaterals and orthodiagonal quadrilaterals . [ 2 ]
In general, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite. Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is a rhombus. A rhombus is a tangential quadrilateral. [10] That is, it has an inscribed circle that is tangent to all four sides. A rhombus.
A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram). A square is a limiting case of both a kite and a rhombus. Orthodiagonal quadrilaterals that are also equidiagonal quadrilaterals are called midsquare quadrilaterals. [2]
In Euclidean geometry, a harmonic quadrilateral, or harmonic quadrangle, [1] is a quadrilateral that can be inscribed in a circle (cyclic quadrilateral) in which the products of the lengths of opposite sides are equal. It has several important properties.