Wednesday, November 14, 2012

Heron's formula


Heron's formula

From Wikipedia, the free encyclopedia
This article is about calculating the area of a triangle. For calculating a square root, see Heron's method.

T = \sqrt{s(s-a)(s-b)(s-c)}In geometry, Heron's (or Hero's) formula, named after
Heron of Alexandria,[1] states that the area T of a triangle whose sides have lengths a, b, and c 
where s is the semiperimeter of the triangle:
s=\frac{a+b+c}{2}.
Heron's formula can also be written as:
T={\ \sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)\ \over 16}\,}
T={\ \sqrt{2(a^2 b^2+a^2c^2+b^2c^2)-(a^4+b^4+c^4)\ \over 16}\,}
T=\frac{1}{4}\sqrt{(a^2 + b^2 + c^2)^2 - 2(a^4 + b^4 + c^4)}.
Heron's formula is distinguished from other formulas for the area of a triangle,
 such as half the base times the height or half the modulus of a cross product of two sides,
 by requiring no arbitrary choice of side as base or vertex as origin.

Posted by at
Labels:

No comments:

Post a Comment

Subscribe to: Post Comments (Atom)