Theorem Of Pythagorean Theorem

YTHAGOREAN THEOREM 3

Pythagorean Theorem

Introduction

The purpose of this paper is for grade 9 and grade 10 students in Ontario high schools to know a brief history about the development of the Pythagorean theorem, write a proof of the theorem, solve problems using the Pythagorean theorem, and calculate primitive

Pythagorean triples with one odd and one even number.

The theorem is called by dierent names: Pythagoras' theorem, the hypotenuse theorem or Euclid I 47, so called because it is listed as Proposition 47 in Book I of Euclid's Elements.

The theorem states that in a right-angled triangle, the area of the square on the hypotenuse, the side opposite the right angle, is equal to the sum of the areas of the squares on the other two sides.

So as a young man, he also travelled to Arabia, Phoenicia, Babylon, and India in order to collect all the mathematical knowledge he could.

When Pythagoras came to Croton, on the southeast coast of modern Italy, he opened a philosophical school. The Pythagorean motto, carved above the entrance of the school, was

\All is number." The school had many followers, both men and women, who were called mathematikoi. They were bounded by oath not to share the teaching or secrets of the school. All discussions were kept a secret. He wrote nothing himself. He did not write any

PYTHAGOREAN THEOREM 8 books. There are several books which were ascribed to Pythagoras, but they were forged in

Pythagoras' name (Human, 2014). The Greek writers Plato, Aristotle, and Dicaearchus do not mention Pythagoras' work in mathematics. It was Eudemus (ca. 370 to 300 BCE) who reported that two propositions, which are later found in Euclid's Elements, were discoveries of the Pythagoreans, but he does not assign the discoveries to any specic Pythagorean

(Human, 2014). Knowledge about him is vague and uncertain. It is thought that

Indeed, it is by no means clear whether any of the theorems ascribed to him were in fact solved by Pythagoras personally or by his followers (Motz, 1993).

Our knowledge of Pythagoras' views is entirely derived from the reports of others. What we know about Pythagoras comes to us from the writings of Iamblichus (who was born around 250 to 330 CE), Porphyry (233 to 309 CE), and Diogenes Laertius (200 to 250 CE), about 750 years after his death. It raises the question of how accurate their works are about the events and people in Pythagoras' life. All the work was written at the time when

Pythagoras achievements were overstated or gloried, as he had in uential philosophies in the West.

If you look at the timeline, several dierent civilizations knew about the Pythagorean theorem before . We have to wonder whether it is possible Pythagoras borrowed the theory and just passed on to the Greeks, a truth that he learned from the East (Human, 2014).

Perhaps he learned of it from an unknown Hindu or Chinese mathematician, who travelled to the Mediterranean and met him or some Pythagorean and shared the knowledge of the