Rectangle
From Wikipedia, the free encyclopedia
In Euclidean geometry, a rectangle is a quadrilateral with four right angles.
Equivalently, it is an equiangular quadrilateral, but it is not necessarily equilateral.
A rectangle with vertices ABCD would be denoted as 
ABCD.
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[edit] Properties
- All angles are 90 degrees.
- Opposite sides are equal in length.
- Opposite sides are parallel.
- Diagonals are equal in length and bisect each other.
[edit] Area, perimeter, and other facts
If a rectangle has length l and width w
.When the length is equal to the width, the rectangle is a square.
The dual polygon of a rectangle is a rhombus.
The term oblong is occasionally used to refer to a non-square rectangle. [1][2]
A rectangle is a special case of a parallelogram, which has two pairs of parallel opposite sides. A parallelogram, and hence also a rectangle, is a special case of a trapezium (known as a trapezoid in North America), which has at least one pair of parallel opposite sides.
Two rectangles, neither of which will fit inside the other, are said to be incomparable.
[edit] Squared, perfect, and other tiled rectangles
A rectangle tiled by squares, rectangles, or triangles is said to be a "squared", "rectangled", or "triangled" (or "triangulated") rectangle respectively. The tiled rectangle is perfect[3][4] if the tiles are similar and finite in number and no two tiles are the same size. If two such tiles are the same size, the tiling is imperfect. In a perfect (or imperfect) triangled rectangle the triangles must be right triangles.
A rectangle has commensurable sides if and only if it is tilable by a finite number of unequal squares.[5][3] The same is true if the tiles are unequal isosceles right triangles.
The tilings of rectangles by other tiles which have attracted the most attention are those by congruent non-rectangular polyominoes, allowing all rotations and reflections. There are also tilings by congruent polyaboloes.
[edit] See also
[edit] References
- ^ http://www.mathsisfun.com/definitions/oblong.html
- ^ http://www.icoachmath.com/SiteMap/Oblong.html
- ^ a b R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte (1940). "The dissection of rectangles into squares". Duke Math. J. 7 (1): 312–340. doi:. http://projecteuclid.org/euclid.dmj/1077492259.
- ^ J.D. Skinner II, C.A.B. Smith and W.T. Tutte (November 2000). "On the Dissection of Rectangles into Right-Angled Isosceles Triangles". J. Combinatorial Theory Series B 80 (2): 277–319. doi:.
- ^ R. Sprague (1940). "Ũber die Zerlegung von Rechtecken in lauter verschiedene Quadrate". J. fũr die reine und angewandte Mathematik 182: 60–64.
[edit] External links
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Wikimedia Commons has media related to category: Rectangles |
- Weistein, Eric W., "Rectangle" from MathWorld.
- Definition and properties of a rectangle With interactive animation
- Area of a rectangle with interactive animation
