A closed planar quadrilateral with opposite sides of equal lengths and , and with four right angles. The area of the rectangle is

and its polygon diagonals and are of length

A square is a degenerate rectangle with .

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).

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.

CITE THIS AS:

Weisstein, Eric W. "Rectangle." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Rectangle.html