Pythagoras

AimAimTo gain an understanding about

Pythagoras and Pythagoras Theorem

swift sonya

Activity 1Activity 1Can your 3 squares fit together

to create a right angled triangle in the centre?

Compare…Compare…the area of the largest square

with the sum of the areas of the two smaller squares.

When might Pythagoras Theorem be useful in real life?When might Pythagoras Theorem be useful in real life?

PythagorasPythagoras570 – 490 BCBorn on the island of Samos,

Greece

Modern view of Pythagoras – Mathematician and scientist

Traditional view of Pythagoras - Philosopher

Deeply religious (he created a way of life) Mystical

Pythagoras’ TeachersPythagoras’ TeachersAnaximander – a ‘scientist and

philosopher’. He believed that the world consisted of one element the ‘Unbounded’ and it was infinite, timeless and indestructible.

Pherecydes – a ‘philosopher and teller of fairy tales’. He believed in metempsychosis (the transmigration of souls).

Pythagoras’ TravelsPythagoras’ TravelsDuring his travels, Pythagoras learned

about mathematical developments and religion.

He travelled to Egypt*, Babylonia*, and maybe as far as India.

Pythagoras eventually settled in Croton, a Greek town in Southern Italy, around the age of 40 where he did most of his philosophical work.

*Note: Before Pythagoras, Ancient Egyptians could create a right angled triangle (lengths = 3, 4, 5) with a piece of rope with 12 knots in it. Ancient Babylonians also knew about the relationship of the 3, 4, 5 triangle!

Pythagorean BrotherhoodPythagorean BrotherhoodPythagoras founded the Pythagorean

Brotherhood, a religious and secretive group with around 600 members.

All is number was the fundamental principle.

Members consisted of two groups the ‘mathematicians’ and the ‘listeners’.

Pythagoras was the leader and his followers became his disciples.

If a secret was revealed the punishment was death.

Religion Religion All is number – numbers were the answer to

everything in the universe and had deep religious significance.

(all numbers had characteristics – e.g. odd numbers were male)

Metempsychosis – all souls have eternal life.The pentagram was their secret sign.The dodecahedron was the shape of the

universe.Forbidden to eat beans.

ProofProofDid Pythagoras create the famous

Theorem?

Sources suggest that he probably didn’t but that he did find the proof that it works.

Pythagoras created proof in mathematics, irrational numbers and 4 platonic solids. (tetrahedron, octahedron, cube and dodecahedron)

There is no written evidence of Pythagoras’ work (although there are fakes!)

Platonic Solids