Difference between revisions of "Heron formula"
From Encyclopedia of Mathematics
(Importing text file) |
(details) |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | A formula expressing the surface area | + | {{TEX|done}} |
| + | 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.). | ||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry", '''1–2''', Springer (1987) (Translated from French) {{ZBL|1153.51001}}</TD></TR> | ||
| + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> H.S.M. Coxeter, "Introduction to geometry", Wiley (1961) {{ZBL|0095.34502}}</TD></TR> | ||
| + | </table> | ||
Latest revision as of 18:02, 17 April 2023
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.).
References
| [a1] | M. Berger, "Geometry", 1–2, Springer (1987) (Translated from French) Zbl 1153.51001 |
| [a2] | H.S.M. Coxeter, "Introduction to geometry", Wiley (1961) Zbl 0095.34502 |
How to Cite This Entry:
Heron formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Heron_formula&oldid=14041
Heron formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Heron_formula&oldid=14041
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article