Pythagoras, often known as Pythagoras of Samos, was a Greek philosopher and mathematician. He is remembered for his contributions to geometry, to be later mentioned. In [1], it states he was born on the island of Samos in the Aegean Sea, in about 569 BC. When Pythagoras moved to Crotona, he shared his ideas of religion and philosophy with roughly 300 people. (According to [1])

According to [4], Pythagoras' father was called Mnesarchus, and his mother Pythais, a native of Samos. Mnesarchus was a merchant from Tyre. Pythagoras had no relative who made any discoveries about mathematical problems.

Thales and his pupil Anaximander who both lived on Miletus were two of the philosophers who influenced Pythagoras. In [3], it states that Pythagoras visited Thales when he was between 18 and 20 years old. At this time, Thales would have been an old man and probably not have taught his a great deal. However, he advised Pythagoras to travel to Egypt to learn more about mathematics and astronomy. Therefore, Pythagoras visited Egypt in 535 BC. Accounts of his journey in Egypt state that he visited many temples and was involved in lots of conversations with the priests.

Pythagoras founded a philosophical and religious school in Croton. (The East of the heel in Southern Italy, its modern name is Crotone) Te followers were known as Mathematikoi, and according to [4], lived permanently with the society, had no personal possessions and were vegetarian.

Some of the beliefs that Pythagoras held were:

1. That at it's deepest level, reality is mathematical in nature

2. That philosophy can be used for spiritual purification

3. That the soul can rise to union with the divine

4. That certain symbols have a mystical significance

However, all of Pythagoras' discoveries originated from his interest in geometry and equations. He studied properties of numbers tat are sill familiar to mathematicians to this day, such as triangle, square and perfect numbers, and also simply odd and even numbers! Another origin included the vibrating strings on the lyre. He noticed that the vibrating strings produced harmonic tones when the ratios of the lengths of the strings were whole numbers. This ideal led to the ability to produce harmonic sound on other string instruments; therefore he also had a massive contribution to musical theory, as well as geometry and mathematical equations.

Through [7], these are some of the "less well known" theorems/ideas produced by Pythagoras.

The sum of the angles of a triangle is equal to two right angles. Also, he calculated the generalisation which states that a polygon with n sides has the sum of interior angles 2n-4 right angles and sum of exterior angles is 4 right angles.

Constructing figures of a given area and geometrical algebra. For example, he solved equations such as a(a-x)=x2 by geometrical means.

The discovery of irrationals. Pythagoras came to this theorem because f his belief that all things are numbers. Naturally, he set a task to prove that the hypotenuse (the side of a right triangle opposite the right angle) of a right angled triangle of an isosceles right angled triangle had a length corresponding to a number.

The five regular solids: tetrahedron, octahedron, icosahedron, hexahedron or cube and the dodecahedron. According to [5], it is thought that Pythagoras himself knew how to construct the tetrahedron, the icosahedron and the octahedron, but it is unlikely he could construct the hexahedron and the dodecahedron.

In astronomy, Pythagoras taught that the Earth was a sphere at the centre of the universe, He was also one of the first to recognise that the orbit of the moon was inclined to the equator of the Earth and that Venus was the same 'thing' when seen at dusk and dawn (as it can not be seen in the middle of the night).

But, above all of his other theorems, he is most famous and well known for his theorem to do with triangles. His theory [6] is a statement that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its two over sides. The area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the lets. Pythagoras proved that if triangle ABC is a triangle with a right angle at C, then a2+b2=c2. The big difference between this and sin, cos and tan is that [7] Pythagoras' theorem does not involve any angles; it just uses 2 sides to find the third side. Sin, cos and tan always involves angles.