Difference between revisions of "Bretschneider's formula"

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Let us have a [[quadrilateral]] with side lengths <math>a,b,c,d</math>, and diagonals<math>p, q</math>. Bretschneider's formula says that
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Let us have a [[quadrilateral]] with side lengths <math>a,b,c,d</math>, and diagonals <math>p, q</math>. Bretschneider's formula says that
 
<math>[ABCD]=\frac{1}{4}*\sqrt{4p^2q^2-(b^2+d^2-a^2-c^2)^2}</math>.
 
<math>[ABCD]=\frac{1}{4}*\sqrt{4p^2q^2-(b^2+d^2-a^2-c^2)^2}</math>.
 
It is derived through [[vector]] geometry.
 
It is derived through [[vector]] geometry.

Revision as of 16:41, 21 June 2006

Let us have a quadrilateral with side lengths $a,b,c,d$, and diagonals $p, q$. Bretschneider's formula says that $[ABCD]=\frac{1}{4}*\sqrt{4p^2q^2-(b^2+d^2-a^2-c^2)^2}$. It is derived through vector geometry.