Encyclopedia > Heron's formula

  Article Content

Heron's formula

In geometry, Heron's formula states that the area of a triangle whose sides have lengths a, b, c is

<math>\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}</math>

where

<math>s=\frac{a+b+c}{2}</math>

This formula is credited to Heron of Alexandria, although it is possible that it may have been known long before Heron's time.

The formula is in fact a special case of Brahmagupta's formula for the area of a cyclic quadrilateral; both of which are special cases of Bretschneider's formula[?] for the area of a quadrilateral.

Expressing Heron's formula with a determinant in terms of the squares of the distances between the three given vertices,

<math> A = \sqrt{ \frac{1}{16} \begin{bmatrix}
  0 & a^2 & b^2 & 1 \\
a^2 & 0 & c^2 & 1 \\ b^2 & c^2 & 0 & 1 \\
  1 &   1 &   1 & 0
\end{bmatrix} } </math>, illustrates its similarity to Tartaglia's formula for the volume of a four-simplex.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Urethra

... is a form of abnormal development of the urethra in the male, where the opening is not quite where it should be (it occurs lower than normal in hypospadias). A ...

 
 
 
This page was created in 24 ms