Pythagoras and His works

Pythagoras was a Greek mathematician who contributed much to the mathematical world, mainly because of Pythagorean Theorem. The following PPT contains all the necessary information about Pythagoras's early and later life, as well as about his works and explanations.(If you find the fonts a little weird, its not my fault as Slideshare doesn't supports many fonts)

1. ROHAN KARMAKAR

2. PYTHAGORAS Pythagoras was an Ionian Greek philosopher,  mathematician. Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which bears his name.

3. WHO WAS PYTHAGORAS ? Pythagoras of Samos was a Greek mathematician and philosopher (570 – 495 BC ). He is known for the proof of the important Pythagorean theorem . He had a great impact on mathematics, theory of music and astronomy. He was an influence for Plato. PYTHAGORAS DEPICTING HIS TETRACTYS

4. Early life Pythagoras spent most of his early childhood at Samos. At first, he studied from the scholars of Syria. His meeting with Thales elicited in him an interest in science, mathematics and astronomy. He then went to Babylon and began to study mathematics. PYTHAGORAS DURING HIS EARLY LIFE

5. LATER LIFE The Pythagoreans, as the followers of Pythagoras were called. They lived and worked at the school. Like most geniuses, Pythagoras too created many enemies. One of them instigated the mob against the Pythagoreans and set fire to the building where they were staying. However , Pythagoras was able to escape. He then went to Metapontum and starved himself to death PYTHAGORAS IN HIS SCHOOL

6. Beliefs of PYTHAGORAS He believed that everything could be reduced to numbers and these numbers had their own characteristics. To him 10 was the most complete number because it was made up of the first 4 digits and when written in dot notation, they formed a triangle. He also believed geometry to be the highest form of mathematical studies through which one can explain the physical world.

7. WORKS OF PYTHAGORAS

8. PYTHAGOREAN THEOREM It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. i.e. where a and b are adjacent sides opposite to the hypotenuse which is c.  

9. Proof of Pythagorean theorem The two large squares shown in the figure each contain four identical triangles, and the only difference between the two large squares is that the triangles are arranged differently. Therefore, the white space within each of the two large squares must have equal area. Equating the area of the white space yields the Pythagorean theorem.  

10. This can be more easily understood by this…: Proof of Pythagorean theorem

11. Uses of PYTHAGOREAN theorem The Pythagorean theorem occurs in the following: In Engineering Calculations In Oceanography (determining speed of sound in water and related uses) It is also used in aerospace industry. It is also used in meteorology and geology.

12. PYTHAGOREAN TRIPLETS Pythagorean triple consists of 3 positive integers a, b, and c, such that . Such a triple is commonly written (a, b, c ). Pythagorean triple is one in which and are coprime. Some examples are :  

13. This can be more easily understood by this…: PYTHAGOREAN TRIPLETS

14. GENERATING A TRIPLET Though the idea of triplet was primarily given by Pythagoras, the idea and mathematical generation of triplets was given by Euclid. Euclid's formula is a fundamental formula for generating Pythagorean triples given an arbitrary pair of integers m and n with . The formula states that the integers. form a Pythagorean triple. The triple generated by Euclid's formula is primitive if and only if  m  and  n  are coprime and not both odd.  

15. PYTHAGOREAN Tetractys The tetractys is a triangular figure consisting of ten points arranged in four rows which is the geometrical representation of the fourth triangular number. AN EXAMPLE OF PYTHAGORAS TETRACTYS HAVING 10 DOT STRUCTURE

16. Uses of PYTHAGOREAN Tetractys The tetractys occurs (generally coincidentally) in the following: The baryon decuplet An archbishop's coat of arms The arrangement of pins in ten-pin bowling A Chinese checkers board The "Christmas Tree" formation in association football

17. All GOOD THINGS Must come to an end ! thanks © Rohan Karmakar (original)