Heros and Brahmaguptas Formulas Lesson 11 8 Hero

Hero’s and Brahmagupta’s Formulas Lesson 11. 8

Hero of Alexandria • He was an ancient Greek mathematician and engineer who was born in 10 AD. • He invented many different machines. • Steam powered device called an aeolipile. • A vending machine. (When the coin went in, holy water came out. ) • A windwheel operating organ. (This is the first instance of using wind power in history. ) • And many other machines… • His contribution to mathematics was with the imaginary number, a method to compute square roots iteratively and Heron’s Formula for find the area of any triangle.

Hero’s Formula: Used to calculate the area of any triangle. a Theorem 111: A∆ = Where a, b, c are length’s of the sides and s = semi-perimeter S=a+b+c 2 b c

=4 Find the area of a triangle with sides 3, 6, and 7. First find the simiperimeter: S=3+6+7 2 S=8

Substitute into Hero’s Formula. A=

• Brahmagupta lived between 598 and 668 AD in India. • He was an Indian mathematician and astronomer. • He was first to use zero as a number. • He was first to say that two negative numbers multiplied together equal a positive number. • He gave the solution to the general linear equation. • He gave two solutions to the general quadratic equation. • He finds Pythagorean triples. • He created the Brahmagupta Formula. • He created or discovered many other things in math.

Brahmagupta’s Formula is a way to find the area of an inscribed quadrilateral. These are known as cyclic quadrilaterals. Theorem 112: Acyclic quad = Where a, b, c, d are sides of the quadrilateral, and s = the semiperimeter.

Brahmagupta’s Formula Find the area of the inscribed quadrilateral. Show all steps. 6 First find the semi-perimeter. 7 2 9 S=7+6+2+9 2 S = 12 Substitute into Brahmagupta’s Formula & solve.

A=