In geometry, Bretschneider's formula is a mathematical expression for the area of a general quadrilateral, and it works for both convex and concave quadrilaterals whether or not they are cyclic.
Facts
StatementThe area K of a general quadrilateral with sides a, b, c and d, semiperimeter s, and opposite angles alpha and gamma equals the square root of the quantity (s-a)(s-b)(s-c)(s-d) minus abcd times the square of the cosine of half the sum of alpha and gamma. 1 Classification
Statement Form Bretschneider's Formula
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Source Bretschneider's formula, Wikipedia
Principal Result Of
Source Wikipedia: Carl Anton Bretschneider
Proved By
Source Bretschneider's formula, Wikipedia
Sources
1. Bretschneider's formula, Wikipedia
History
The German mathematician Carl Anton Bretschneider discovered the formula in 1842.
History section
The German mathematician Carl Anton Bretschneider discovered the formula in 1842.
In Branch: Geometry, Lead sentence
In geometry, Bretschneider's formula is a mathematical expression for the area of a general quadrilateral.
Proved By: Carl Anton Bretschneider, Lead
The German mathematician Carl Anton Bretschneider discovered the formula in 1842.
View the SourceWikipedia: Carl Anton Bretschneider
Principal Result Of: Carl Anton Bretschneider, Article textQuote, Principal Result Of: Carl Anton Bretschneider, Article text
He is best known for his discovery of Bretschneider's formula for the area of a general quadrilateral on a plane,
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