Pythagorean theorem
Years ago, a man named Pythagoras
found an amazing fact about triangles:
If the triangle hasa right angle (90°) ...
... and you make a square on each of the three sides, then ...
... the biggest square has the exact same area as the other
two squares put together!
It is called "Pythagoras' Theorem" and can be written in one short equation:
a2 + b2 = c2
Note:


c is the longest side of the triangle
a and b are the other two sides
The longest side of the triangle is called the
"hypotenuse", so the formal definition is:
In a right angled triangle:
the square of the hypotenuse is equal to
the sum of the squares of the other two sides.
Samos, Kroton and Pythagoras
Pythagoras, born on the Aegean island of Samos in the 6th century
B.C. and active in southern Italy, was an ancient Greek philosopher
and mathematician best known for a theorem in geometry that was
named for him. Pythagoras is credited with founding a philosophical
school that deviated from the male-dominated Greek norms by
allowing women to participate equally. The teachings of the school
aren't strictly what we think of as philosophical. They also include
rules on living and what to eat. Supposedly, the Pythagoreans
explained the common human physiological response to beans as a
spirit trying to exit the body. Therefore bean-consumption was taboo.
Pythagoras is also associated with the theory of metempsychosis in
which the soul of the dead is reborn into another body.
Pythagoras and the Pythagorean Theorem:
Pythagoras is most familiar to students of geometry for a theorem that bears his name. The
Pythagorean Theorem says that the square of the hypoteneuse of a right triangle is equal to the sum
of the squares of each of the other two sides or A2 + B2 = C2.
Samos and Croton
Pythagoras Migrates From Samos to Croton:
A native of the Aegean island of Samos, a powerful,
technologically advanced Ionian city-state, Pythagoras
opposed the regime of Polycrates, a tyrant who came to
power in the 530s. In 530 Pythagoras left and took up
residence in Croton, in the south of Italy, a city known for its
athletes and doctors.
Temple of Hera in Croton
Pythagoras Quotation:
"Once, they say, he [Pythagoras] was passing by when a dog was being ill-treated. 'Stop!' he said,
'don't hit it! It is the soul of a friend! I knew it when I heard its voice." - Xenophanes
Samos:
Samos (Greek: Σάμος) is a Greek island in the eastern Aegean Sea, south of Chios, north of Patmos
and the Dodecanese, and off the coast of Asia Minor, from which it is separated by the 1.6kilometre (1.0 mi)-wide Mycale Strait. It is also a separate regional unit of the North Aegeanregion,
and the only municipality of the regional unit.
In ancient times Samos was a particularly rich and
powerful city-state. It is home to Pythagoreion and the
Diadema di Capocolonne
Heraion of Samos, a UNESCO World Heritage Site that
includes the Eupalinian aqueduct, a marvel of ancient
engineering. Samos is the birthplace of the Greek
philosopher and mathematician Pythagoras, after whom
the Pythagorean theorem is named, the philosopher
Epicurus, and the astronomer Aristarchus of Samos, the
first known individual to propose that the Earth
revolves around the sun. Samian wine was well known
in antiquity, and is still produced on the island.
The history of Samos in the Pre-historic times is close joint with the
goddess Hera which was believed to had been born in the island
and for her sake Ionians built in the 7th century BC, the famous
Temple of Hera, on the ruins of an earlier prehistoric temple.
The beginning of its history is lost in time. We do not know exactly
when it was first inhabited but it is believed that it was inhabited as
far as back as the Neolithic years (3rd millennium BC). Historians
say that the first colonists of the island were Phoenicians, Leleges
and Carians and also mention the Pelasgians, who brought to the
island the worship of the goddess Hera. The place - names Samos,
Imrrassos, Chesios and Astypalaia show a connection with Asia
Minor and the languages of the Leleges and Carias.
The first colonists from Asia Minor were followed in later years by
a wave of Myceneans which are traditionally supposed to have been
the companions of the mythical kingAngaeus (1.300 BC). A monarch who had taken part in the
Argonaut expedition and who was recognized by all the ancient authorities as the founder of the city
of Samos.
Temple of Hera in Samos
The history of Samos in the Pre-historic times is close joint with the goddess Hera which was
believed to had been born in the island and for her sake Ionians built in the 7th century BC, the
famous Temple of Hera, on the ruins of an earlier prehistoric temple.
Samos reached its pinnacle during the period it was governed by the tyrant Polycrates (532 - 522
BC). It was then that Samos grew into a great naval power and founded its own colonies. A new
kind of ship was constructed in the shipyards on the island with 50 oars, the famous samaina.
Samos which constituted the bridge between Greece and East, managed for many years, because of
its power, to remain independent, while at the same time flourishing, despite the battles that were
waged to conquer it. That was perhaps one of the reasons that caused Samos to produce so many
men of genius as well as great artists such as the astronomer and mathematician Aristarchus, who
was the first to study the movement of the earth.
We should also mention Callistatus, who
was responsible for founding or
establishing the 24 - letter alphabet, the
architects and sculptors Rhoikos and
Theodoros, who built the famous temple
of Hera and the painters Saurias (the first
painter too use chiamoscuro in his work)
and Calliphon, painter of a number of
master works which were to be seen in
the temple of Artemis at Ephesus.But the
most exceptional of all these figures,
is Pythagoras
(580
500
BC)philosopher, mathematician and
musician. He was never a man to take
things for granted, he sought in the
sciences, arts and travel, knowledge and experience which would allow him with certainty, to
assume his place in the intellectual arena of his timesHis genius, combined with deep study and
ascetism allowed him to develop his knowledge to a point which is still of fundamental importance
to mathematical theory and the Pythagorean theorem in geometry is, naturally, still used as are the
Pythagorean tables in arithmetic.
Today, Samos is regarded as one of the most beautiful Hellenic islands. An island which live its
traditions, and this can be felt in every step one takes there and in every meeting with the courteous
and hard - working people of the island who they still follow the steps of their great ancestors.
In the pitch - black nights of winter, when the fishermen pass by the wind-buffeted and sheer slopes
of Mt. Kerkis, the highest mountain of Samos, they say they see a light up to the peak which like a
lighthouse guides them on a safe course during a storm. They even say that the light is the spirit of
Pythagoras