Rectangle

In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles.

From this definition, it follows that a rectangle has two pairs of opposite sides of equal length; that is, a rectangle is a parallelogram. A square is a special kind of rectangle where all four sides have equal length; that is, a square is both a rectangle and a rhombus. A rectangle that is not a square is colloquially known as an oblong.

Of the two opposite pairs of sides in a rectangle, the length of the longer side is called the length of the rectangle, and the length of the shorter side is called the width. The area of a rectangle is the product of its length and its width; in symbols, A = lw. For example, the area of a rectangle with a length of 5 and a width of 4 would be 20, because 5 × 4 = 20. See the picture above right.

In calculus, the Riemann integral can be thought of as a limit of sums of the areas of arbitrarily thin rectangles.

Oblong

The word oblong was once commonly used as an alternate name for a rectangle. In his translation of Euclid's Elements, Sir Thomas Heath translates the Greek word ετερομηκες mekes – literally, "different lengths" in Book One, Definition 22 as oblong. "Of Quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right angled but not equilateral...".

The term 'oblong' is generally not used today in mathematics, as 'rectangle' seems to be more in fashion however the common definition of oblong is that an oblong is an un-equal rectangle and a square is an equal rectangle, rectangle being the shape-group these both fit into. Oblong is also sometimes referred to as the adjectival form of rectangle, just like the word 'rectangular'. All in all, it varies from person to person: the younger generation say rectangle and the older generation usually says oblong.

References

Heath, Sir Thomas L. The Thirteen Books of Euclid's Elements. 2nd ed. 3 vols. 1926; rpt. New York: Dover Publications, Inc., 1956.

Quadrilaterals

Gourt Home::Gourt :: Rectangle

Oblong

See also

References