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Your Email Pythagoras of Samos" redirects here. For the Samian statuary, see [|Pythagoras (sculptor)] . For other uses, see [|Pythagoras (disambiguation)]. Pythagoras (Πυθαγόρας) ||||= Bust of Pythagoras of Samos in the [|Capitoline Museums], [|Rome] || [|Samos Island] || [|Metapontum] ||
 * ~ Full name || Pythagoras (Πυθαγόρας) ||
 * ~ Born || c. 570 BC
 * ~ Died || c. 495 BC (aged around 75)
 * ~ Era || [|Ancient philosophy] ||
 * ~ Region || Western philosophy ||
 * ~ [|School] || [|Pythagoreanism] ||
 * ~ Main interests || [|Metaphysics], [|Music], [|Mathematics], [|Ethics], [|Politics] ||
 * ~ Notable ideas || [|Musica universalis], [|Golden ratio], [|Pythagorean tuning], [|Pythagorean theorem] ||
 * = Influenced by[show] [|Thales], [|Anaximander], [|Pherecydes] ||
 * = Influenced[show] [|Philolaus], [|Alcmaeon], [|Parmenides], [|Plato], [|Euclid], [|Empedocles], [|Hippasus], [|Kepler] ||

Pythagoras made influential contributions to [|philosophy] and religious teaching in the late 6th century BC. He is often revered as a great [|mathematician], [|mystic] and [|scientist], and he is best known for the [|Pythagorean theorem] which bears his name. However, because legend and obfuscation cloud his work even more than with the other [|pre-Socratic philosophers], one can say little with confidence about his teachings, and some have questioned whether he contributed much to [|mathematics] and [|natural philosophy]. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Whether or not his disciples believed that everything was related to mathematics and that numbers were the ultimate reality is unknown. It was said that he was the first man to call himself a philosopher, or lover of wisdom,[|[4]] and Pythagorean ideas exercised a marked influence on [|Plato], and through him, all of [|Western philosophy].
 * Pythagoras of Samos** ([|Ancient Greek]: Ὁ Πυθαγόρας ὁ Σάμιος //Ho Pythagóras ho Sámios// "Pythagoras the [|Samian]", or simply Ὁ Πυθαγόρας; c. 570-c. 495 BC[|[1]]) was an [|Ionian] [|Greek] [|philosopher], [|mathematician], and founder of the religious movement called [|Pythagoreanism]. Most of the information about Pythagoras was written down centuries after he lived, so that very little reliable information is known about him. He was born on the island of [|Samos], and may have travelled widely in his youth, visiting [|Egypt] and other places seeking knowledge. He had a teacher named [|Themistoclea], who introduced him to the principles of ethics.[|[2]][|[3]] Around 530 BC, he moved to [|Croton], a [|Greek colony] in [|southern Italy], and there set up a religious sect. His followers pursued the religious rites and practices developed by Pythagoras, and studied his philosophical theories. The society took an active role in the politics of Croton, but this eventually led to their downfall. The Pythagorean meeting-places were burned, and Pythagoras was forced to flee the city. He is said to have ended his days in [|Metapontum].

[[|hide]] Pythagoras was a mathematician whose findings have stood the test of time. He was born on the Greek island of Samos, located in the eastern Aegean Sea. He lived from 569-475 BC. He was primarily a philosopher. He started many movements outside of mathematics as well. He also founded the religious movement called Pythagoreanism in addition to his movements in philosophy, mathematics, and science. - Tayler and Brittany.  =Pythagoras' Theorem= > //If the triangle had a right angle (90°) ...// > //... and you made a square on each of the three sides, then ...// > //... the biggest square had the **exact same area** as the other two squares put together!// ||  ||
 * ==Contents==
 * [|1 Biographical sources]
 * [|2 Life]
 * [|3 Writings]
 * [|4 Mathematics]
 * [|4.1 Pythagorean theorem]
 * [|4.2 Musical theories and investigations]
 * [|4.3 Tetractys]
 * [|5 Religion and science]
 * [|5.1 Lore]
 * [|6 Pythagoreans]
 * [|7 Influence] ||
 * // Years ago, a man named Pythagoras found an amazing fact about triangles: //

a2 + b2 = c2
 * [[image:http://www.mathsisfun.com/geometry/images/pythagoras-abc.gif width="209" height="230" caption="Pythagoras"]] || It is called "Pythagoras' Theorem" and can be written in one short equation:

Note:
 * **c** is the **longest side** of the triangle
 * **a** and **b** are the other two sides ||

Definition
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.

Sure ... ?
Let's see if it really works using an example.

Example: A [|"3,4,5" triangle] has a right angle in it.
32 + 42 = 52 Calculating this becomes: 9 + 16 = 25 //It works ... like Magic!// ||
 * [[image:http://www.mathsisfun.com/geometry/images/pythagoras-3-4-5.gif width="221" height="206" caption="pythagoras theorem"]] || Let's check if the areas **are** the same:

Why Is This Useful?
If we know the lengths of **two sides** of a right angled triangle, we can find the length of the **third side**. (But remember it only works on right angled triangles!)

How Do I Use it?
Write it down as an equation:
 * [[image:http://www.mathsisfun.com/geometry/images/triangle-abc.gif width="180" height="100" caption="abc triangle"]] ||  || a2 + b2 = c2 ||

Now you can use [|algebra] to find any missing value, as in the following examples:

Example: Solve this triangle.
52 + 122 = c2 25 + 144 = c2 169 = c2 c2 = 169 c = √169 You can also read about [|Squares and Square Roots] to find out why √169 = 13
 * [[image:http://www.mathsisfun.com/images/triangle4.gif width="186" height="107" caption="right angled triangle"]] || a2 + b2 = c2
 * c = 13** ||

Example: Solve this triangle.
92 + b2 = 152 81 + b2 = 225 Take 81 from both sides: b2 = 144 b = √144 jesh&andrew
 * [[image:http://www.mathsisfun.com/images/triangle3.gif width="186" height="107" caption="right angled triangle"]] || a2 + b2 = c2
 * b = 12** ||

Example: What is the diagonal distance across a square of size 1?
12 + 12 = c2 1 + 1 = c2 2 = c2 c2 = 2 It works the other way around, too: when the three sides of a triangle make a2 + b2 = c2, then the triangle is right angled.
 * [[image:http://www.mathsisfun.com/images/unit-square-diagonal.gif width="128" height="141" caption="Unit Square Diagonal"]] || a2 + b2 = c2
 * c = √2 = 1.4142...** ||

Example: Does this triangle have a Right Angle?
They are equal, so ... Yes, it does have a Right Angle! ||
 * [[image:http://www.mathsisfun.com/algebra/images/triangle-10-24-26.gif width="165" height="151" caption="10 24 26 triangle"]] ||  || Does a2 + b2 = c2 ?
 * a2 + b2 = 102 + 242 = 100 + 576 = **676**
 * c2 = 262 = **676**

Example: Does an 8, 15, 16 triangle have a Right Angle?
So, NO, it does not have a Right Angle
 * Does 8**2 + **15**2 = **16**2 ?
 * 82 + 152 = 64 + 225 = **289**,
 * but 162 = **256**

Example: Does this triangle have a Right Angle?
Does (**√**3)2 + (**√**5)2 = (**√**8)2 ? Does 3 + 5 = 8 ? Yes, it does! So this **is** a right-angled triangle ||
 * [[image:http://www.mathsisfun.com/algebra/images/triangle-r3-r5-r8.gif width="115" height="163" caption="Triangle with roots"]] ||  || Does a2 + b2 = c2 ?