A closed planar quadrilateral with opposite sides of equal lengths
and , and with four right
angles . A square is a degenerate rectangle with .

The area of the rectangle is

(1)

and its polygon diagonals and
are of length

(2)

A rectangle has a circumcircle with circumradius

(3)

but incircle only in the degenerate case of a square .

A number of important topological surfaces can be constructed from the rectangle. Gluing both pairs of opposite edges together with no twists gives a torus ,
gluing two opposite edges together after giving a half-twist gives a Möbius
strip , gluing both pairs of opposite edges together giving one pair a half-twist
gives a Klein bottle , and giving both pairs a half-twist
gives a projective plane (Stewart 1997).

See also Blanche's Dissection ,

Fault-Free Rectangle ,

Golden
Rectangle ,

Incomparable Rectangles ,

Klein Bottle ,

Möbius
Strip ,

Overlapping Rectangles ,

Perfect
Rectangle ,

Projective Plane ,

Rectangle
Tiling ,

Rectellipse ,

Rounded
Rectangle ,

Square ,

Torus Explore this topic in
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References Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 122,
1987. Eppstein, D. "Rectilinear Geometry." http://www.ics.uci.edu/~eppstein/junkyard/rect.html . Fukagawa,
H. and Pedoe, D. "Circle and Rectangles." §3.4 in Japanese
Temple Geometry Problems. Winnipeg, Manitoba, Canada: Charles Babbage Research
Foundation, pp. 43-44 and 125, 1989. Harris, J. W. and Stocker,
H. "Rectangle." §3.6.5 in Handbook
of Mathematics and Computational Science. New York: Springer-Verlag, p. 84,
1998. Kern, W. F. and Bland, J. R. Solid
Mensuration with Proofs, 2nd ed. New York: Wiley, p. 2, 1948. Stewart,
I. "Squaring the Square." Sci. Amer. 277 , 94-96, July 1997.
Cite this as:
Weisstein, Eric W. "Rectangle." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Rectangle.html

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