“Brahmagupta's Formula”的概念、定义、习题解题方法及翻译-数学辞典

单词

Brahmagupta's Formula

释义

Brahmagupta's Formula

For a Quadrilateral with sides of length , , , and , the Area is given by

(1)

where

(2)

is the Semiperimeter,

is the Angle between

and

, and

is the Angle between

and

.For a Cyclic Quadrilateral (i.e., a Quadrilateral inscribed in a Circle),

, so

			(3)
			(4)

where

is the Radius of the Circumcircle. If the Quadrilateral is Inscribed in one Circleand Circumscribed on another, then the Area Formula simplifies to

(5)

See also Bretschneider's Formula, Heron's Formula

References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 56-60, 1967.

Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 81-82, 1929.

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