1. Hero’s and Brahmagupta’s Formulas Lesson 11.8

2. 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.

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

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

5. A= Substitute into Hero’s Formula.

6. 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.

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

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

9. A=