Heron

Heron

1. Heron By Yashank, Samarth, Priyansh, Purva , Muskaan

2. Heron   Heron   of Alexandria   (c. 10–70 AD) was an ancient Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. He is considered the greatest experimenter of antiquity and his work is representative of the Hellenistic scientific tradition.

3. Heron Heron published a well recognized description of a steam-powered device called an  aeolipile  (hence sometimes called a "Hero engine"). Among his most famous inventions was a  windwheel , constituting the earliest instance of wind harnessing on land.  He is said to have been a follower of the Atomists. Some of his ideas were derived from the works of  Ctesibius . Much of Hero's original writings and designs have been lost, but some of his works were preserved in Arab manuscripts

4. History The formula is credited to Heron of Alexandria, and a proof can be found in his book,  Metrica , written in A.D. 60. It has been suggested that Archimedes knew the formula over two centuries earlier, and since  Metrica  is a collection of the mathematical knowledge available in the ancient world, it is possible that the formula predates the reference given in that work. A formula equivalent to Heron's namely: T 1/2 , where   was discovered by the Chinese independently of the Greeks.  

5. What is Heron’s Formula ? Heron's formula is named after Heron of Alexendria , a Greek Engineer and Mathematician in 10 - 70 AD. You can use this formula to find the  area of a triangle  using the 3 side lengths.  Therefore, you do not have to rely on  the formula for area that uses base and height .

6. Area of Equilateral triangle By Pythagoras theorem: a 2  = (a/2) 2  + h 2 a 2  = a 2 /4 + h 2 a 2  − a 2 /4 = h 2 4a 2 /4 − a 2 /4 = h 2 3a 2 /4 = h 2 h = √(3a 2 /4)  h = (√(3)×a)/2 Area = (base × h)/2  base × h = (a × √(3)×a)/2 = (a 2 × √(3))/2 Dividing by 2 is the same as multiplying the denominator by 2. Therefore, the formula is )/4  

7. Area of Scalene Triangle In this triangle it is impossible to find the height which is necessary to find the are by the formula: ½ x (height) x(base) a b c

8. The Heron’s Formula You can use Heron's formula to calculate the area of any triangle when you know the lengths of the three sides. If you call the lengths of the three sides a, b, and c, the formula is : with “S is the semi-perimeter”  

9. Example For Heron’s Formula Use Heron's formula to find the area of triangle ABC Ans . Step 1 Calculate the semi perimeter, S S = (3+2+4) /2 S = 9/2 = 4.5 Step 2 Substitute S into the formula 2.9   A B C 3 2 4

10. Thanks