Rectangle -- from Wolfram MathWorld
- ️Weisstein, Eric W.
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, Perfect Rectangle, Projective Plane, Rectangle Tiling, Rectellipse, Rounded Rectangle, Square, Torus Explore this topic in the MathWorld classroom
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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.
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Cite this as:
Weisstein, Eric W. "Rectangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Rectangle.html