Rhombus
Rhombus
A rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides the same length, i.e., an equilateral parallelogram. The word rhomb is sometimes used instead of rhombus, and a rhombus is sometimes also called a diamond. A rhombus with 2theta=45 degrees is sometimes called a lozenge.
The polygon diagonals p and q of a rhombus are perpendicular and satisfy
| p^2+q^2=4a^2. |
(1)
|
The diagonals are related to the opening angle theta by
p = 2acostheta
(2)
q = 2asintheta.
(3)
The area of a rhombus is given by
A = 1/2pq
(4)
= 2a^2costhetasintheta
(5)
= a^2sin(2theta).
(6)
The rhombus is a tangential quadrilateral with a=b=c=d, and so has inradius
r = [画像:(pq)/(2sqrt(p^2+q^2))]
(7)
= 1/2asin(2theta).
(8)
See also
Diamond, Golden Rhombus, Harborth's Tiling, Kite, Lozenge, Necker Cube, Parallelogram, Quadrilateral, Rhombic Dodecahedron, Rhombic Hexecontahedron, Rhombic Icosahedron, Rhombic Triacontahedron, Rhombohedron, Rhomboid, Skew Quadrilateral, Trapezium, TrapezoidExplore with Wolfram|Alpha
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References
Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 123, 1987.Harris, J. W. and Stocker, H. "Rhombus." §3.6.4 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, pp. 83-84, 1998.Kabai, S. and Bérczi, S. Rhombic Structures: Geometry and Modeling from Crystals to Space Stations. Püsspökladány, Hungary: Uniconstant, 2015.Referenced on Wolfram|Alpha
RhombusCite this as:
Weisstein, Eric W. "Rhombus." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Rhombus.html