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