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1. Art Integrated Project of math’s
 Name – Mohit sharma
 Class – 12th
 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 Samos. 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.
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2

9. Proof Of Pythagoras theorem
 A right-angled triangle ABC, right-angled at B.
 To Prove- AC2 = AB2 + BC2
 Construction: Draw a perpendicular BD meeting AC at D
Proof:
We know, △ADB ~ △ABC
Therefore, ADAB=ABAC (corresponding sides of similar triangles)
Or, AB2 = AD × AC ……………………………..……..(1)
Also, △BDC ~△ABC
Therefore, CDBC=BCAC (corresponding sides of similar triangles)
Or, BC2= CD × AC ……………………………………..(2)
Adding the equations (1) and (2) we get,
AB2 + BC2 = AD × AC + CD × AC
AB2 + BC2 = AC (AD + CD)
Since, AD + CD = AC
Therefore, AC2 = AB2 + BC2
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.