Heron's formula

Heron's formula gives the area of a triangle when the lengths of all three sides are known. Given the lengths of the three sides of a triangle, a, b, c, the area of the triangle can be determined as

A = \sqrt{s(s-a)(s-b)(s-c)}

where s = \dfrac{a+b+c}{2} , semi-perimeter of the triangle.

The formula can be transformed to the following interesting forms.

Division of Radicals

\dfrac{\sqrt[n]{x}}{\sqrt[n]{y} }

Multiplication of Radicals

\sqrt[n]{x}\cdot \sqrt[n]{y}

Definition of Derivative

Let f(x) contains an open interval containing x_0 in its domain, the function is differentiable if the limit

L = \lim\limits_{\Delta x \to0} \dfrac{f(x_0+\Delta x )-f(x)}{\Delta x }

exist.