Pythagoras: Pythagoras
Biography: Biography Pythagoras was born in 572BC on the island of Samos, Greece. In about 530BC Pythagoras left Samos in hatred for its ruler Polycrates and settled in Cretona, Italy. He joined a religious group known as the Pythagoreans. He formed a philosophical and religious school where they studied mathematics, science and music. This attracted many followers. When involved with this group he discovered what is now known as Pythagoras’ Theorem. Also during his time there he out the mathematics of octaves and harmony. Because of the secrecy in the group there is nothing of Pythagoras’ writings or books. Pythagoras was murdered at the age of 77, in 495BC and the religious school was separated.
Relevance: Relevance Pythagoras is often described as one of the pure mathematicians of his time and an extremely important figure in the expansion of mathematics. Pythagoras’ theorem is studied from Year 8 to Year 12 in NSW schools. Students today often wonder why geometry is so important. It allows people to think more logically and as I have shown in Contemporary Importance his theorem is used in numerous jobs and work areas. Students pursuing technical majors in college are expected to understand and extend this knowledge on geometry. Geometry proofs are also an important way to increase disciplined . As you can see geometry is still just as important now as it was in Pythagoras’ time.
Pythagoras: Pythagoras Lived in southern Italy during the sixth century B.C. Considered the first true mathematician Used mathematics as a means to understand the natural world First to teach that the earth was a sphere that revolves around the sun
Slide 5: About 2,500 years ago, a Greek mathematician named Pythagorus discovered a special relationship between the sides of right triangles.
Slide 6: a b c
Mathematical achievements: Mathematical achievements Pythagoras has contributed various theories to geometry, algebra, number .etc. All of these theories were discovered during Pythagoras’ time with the Pythagoreans. Pythagoras’ theory is : The square on the hypotenuse in any right-angled triangle is equal to the sum of the squares on the other two sides. So for example: A B C a b c 4 3 c Using the formula a ²+b²=c² find side “c” on the triangle DEF D E F 4 ² + 3² = c² 16 + 9 = c² 25 = c² √25 = c² c = 5
The Pythagorean Theorem: The Pythagorean Theorem “For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.” a 2 + b 2 = c 2
Proof: Proof
Baseball Problem: Baseball Problem A baseball “diamond” is really a square. You can use the Pythagorean theorem to find distances around a baseball diamond.
Baseball Problem: Baseball Problem The distance between consecutive bases is 90 feet. How far does a catcher have to throw the ball from home plate to second base?
Baseball Problem: Baseball Problem To use the Pythagorean theorem to solve for x, find the right angle. Which side is the hypotenuse? Which sides are the legs? Now use: a 2 + b 2 = c 2
Baseball Problem Solution: Baseball Problem Solution The hypotenuse is the distance from home to second, or side x in the picture. The legs are from home to first and from first to second. Solution: x 2 = 90 2 + 90 2 = 16,200 x = 127.28 ft
Slide 14: MADE BY-RIJUL SETHI CLASS-10-A SCHOOL-ARMY PUBLIC SCHOOL