Namespaces
Variants
Actions

Difference between revisions of "Heron formula"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(TeX)
Line 1: Line 1:
A formula expressing the surface area <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471201.png" /> of a triangle in terms of its sides <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471202.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471203.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471204.png" />:
+
{{TEX|done}}
 +
A formula expressing the surface area $S$ of a triangle in terms of its sides $a$, $b$ and $c$:
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471205.png" /></td> </tr></table>
+
$$S=\sqrt{p(p-a)(p-b)(p-c)},$$
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h047/h047120/h0471206.png" />. Named after Heron (1st century A.D.).
+
where $p=(a+b+c)/2$. Named after Heron (1st century A.D.).
  
  

Revision as of 21:16, 11 April 2014

A formula expressing the surface area $S$ of a triangle in terms of its sides $a$, $b$ and $c$:

$$S=\sqrt{p(p-a)(p-b)(p-c)},$$

where $p=(a+b+c)/2$. Named after Heron (1st century A.D.).


Comments

References

[a1] M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French)
[a2] H.S.M. Coxeter, "Introduction to geometry" , Wiley (1961)
How to Cite This Entry:
Heron formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Heron_formula&oldid=31574
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article