“Area”的概念、定义、习题解题方法及翻译-数学辞典

单词

Area

释义

Area

The Area of a Surface is the amount of material needed to ``cover'' it completely. The Area of a Triangle isgiven by

(1)

where

is the base length and

is the height, or by Heron's Formula

(2)

where the side lengths are

, and

and

the Semiperimeter. The Area of a Rectangle isgiven by

(3)

where the sides are length

and

. This gives the special case of

(4)

for the Square. The Area of a regular Polygon with

sides and side length

is given by

(5)

Calculus and, in particular, the Integral, are powerful tools for computing the Area between a curve and the x-Axis over an Interval , giving

(6)

The Area of a Polar curve with equation

(7)

Written in Cartesian Coordinates, this becomes

			(8)
			(9)

For the Area of special surfaces or regions, see the entry for that region. The generalization of Area to 3-D is calledVolume, and to higher Dimensions is called Content.

See also Arc Length, Area Element, Content, Surface Area, Volume

References

Gray, A. ``The Intuitive Idea of Area on a Surface.'' §13.2 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 259-260, 1993.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。