Heron of Alexandria

Definition

Heron of Alexandria was an ancient Greek mathematician and engineer who is best known for Heron's formula, which calculates the area of a triangle using its side lengths. This formula is particularly useful in trigonometry for dealing with non-right triangles.

5 Must Know Facts For Your Next Test

1. Heron's formula states that the area $A$ of a triangle with sides $a$, $b$, and $c$ is given by $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter $(a+b+c)/2$.
2. Heron's formula can be derived using the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
3. Heron was also known for his work in geometry and mechanics, including inventions like the aeolipile, an early steam engine.
4. In algebra and trigonometry, Heron’s formula helps solve problems involving non-right triangles where height cannot be easily determined.
5. Understanding Heron's formula requires familiarity with basic algebraic operations and properties of square roots.

Review Questions

• What is Heron's formula for calculating the area of a triangle?
• How does the semi-perimeter relate to Heron's formula?
• Why might Heron's formula be particularly useful when working with non-right triangles?

Related terms

Law of Cosines: The Law of Cosines relates the lengths of the sides of any triangle to the cosine of one of its angles: $$c^2 = a^2 + b^2 - 2ab\cos(C)$$.

Semi-Perimeter: The semi-perimeter, denoted as $s$, is half the perimeter of a triangle: $$s = \frac{a+b+c}{2}$$.

Non-Right Triangle: A triangle that does not contain a right angle (90 degrees).