A closed planar quadrilateral with opposite sides of equal lengths right angles . A square is a degenerate rectangle with
The area of the rectangle is
(1)
and its polygon diagonals
(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 Explore with Wolfram|Alpha References Beyer, W. H. (Ed.). 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 Japanese Temple Geometry Problems. Harris, J. W. and Stocker, H. "Rectangle." §3.6.5 in Handbook of Mathematics and Computational Science. Kern, W. F. and Bland, J. R. Solid Mensuration with Proofs, 2nd ed. Stewart, I. "Squaring the Square." Sci. Amer. 277 , 94-96, July 1997. Referenced on Wolfram|Alpha Rectangle Cite this as: Weisstein, Eric W. "Rectangle." From MathWorld https://mathworld.wolfram.com/Rectangle.html
Subject classifications 
and 
, and with four right angles. A square is a degenerate rectangle with 
. 
and 
are of length 
