Pythagoras and His Works .pptx

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1. Art Integrated Project of math’s Name – Mohit sharma Class – 12 th Section –science (A) Roll no. – 12117 Topic – Pythagoras Subject- math’s

2. Pythagoras and His Works

3. Pythagoras Pythagoras was an ionic greek philosopher mathematician . Pythagoras made influential contributions to philosophy and religion in the late 6h century BC .He is often rewarrd as a great mathematician and scientist and is best for the known Pythagoras theorem.

4. Biography Pythagoras  was  born  in Samos and likely went to Egypt and Babylon as a young man. He emigrated to southern Italy about 532 bce , apparently to escape Samos's tyrannical rule, and established his ethico -political academy at Croton (now Crotone, Italy)

5. Early life Pythagoras spent most of his early childhood at S amos. At first 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.

6. 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 ere staying . However ,Pythagoras was able to escape . He then went to Metpontum and starved himself to death.

7. Pythagoras and Music Pythagoras made important developments in music and astronomy. Observing that plucked strings of different tones, he came up with gave off different tones , he came up with the musical scale still used today. Was an accomplished musician at playing the lyre .

8. Pythagoras Theorem T 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. Hypotenuse 2  = Perpendicular 2  + Base 2   c 2  = a 2  + b 2    

9. Proof Of Pythagoras theorem  A right-angled triangle ABC, right-angled at B. To Prove- AC 2  = AB 2  + BC 2 Construction: Draw a perpendicular BD meeting AC at D Proof: We know, △ADB ~ △ABC Therefore,  ADAB = ABAC  (corresponding sides of similar triangles) Or, AB 2  = AD × AC ……………………………..……..(1) Also, △BDC ~△ABC Therefore,  CDBC = BCAC  (corresponding sides of similar triangles) Or, BC 2 = CD × AC ……………………………………..(2) Adding the equations (1) and (2) we get, AB 2  + BC 2  = AD × AC + CD × AC AB 2  + BC 2  = AC (AD + CD) Since, AD + CD = AC Therefore, AC 2  = AB 2  + BC 2 Hence, the Pythagorean theorem is proved

10. Application of Pythagoras theorem To know if the triangle is a  right-angled triangle  or not. In a right-angled triangle, we can calculate the length of any side if the other two sides are given. To find the diagonal of a square.