### Py·thag·o·ras

### /pəˈTHaɡərəs/

- 1. c. 580–500 bc, Greek philosopher; known as Pythagoras of Samos. Pythagoras sought to interpret the entire physical world in terms of numbers and founded their systematic and mystical study. He is best known for the theorem of the right-angled triangle.

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Pythagoras of Samos (c. 570 BC – 495 BC) was

**an ancient Ionian Greek philosopher and the**epon**ymous founder of**Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy.- c. 570 BC, Samos
- Pre-Socratic philosophy

- c. 495 BC (aged around 75), either Croton or Metapontum
- Western philosophy

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**Pythagoras**: ultimate proofs and crazy contortions

Pythagoras, (born c. 570 bce, Samos, Ionia [Greece]—died c. 500–490 bce, Metapontum, Lucanium [Italy]),

**Greek philosopher, mathematician, and founder of the Pythagorean brotherhood**that, although**religious in nature, formulated principles**that**influenced the thought of Plato and Aristotle**and**contributed to**the**development of ma**thematics and Western rational philosophy.- The Pythagorean Question
- Sources
- Life and Works
- The Philosophy of Pythagoras
- Was Pythagoras A Mathematician Or cosmologist?

What were the beliefs and practices of the historical

**Pythagoras**?This apparently simple question has become the daunting Pythagoreanquestion for several reasons. First,**Pythagoras**himself wrote nothing,so our knowledge of**Pythagoras**’ views is entirely derived from thereports of others. Second, there was no extensive or authoritativecontemporary account of**Pythagoras**. No one did for**Pythagoras**whatPlato and Xenophon did for Socrates. Third, only fragments of thefirst detailed accounts of**Pythagoras**, written about 150 years afterhis death, have survived. Fourth, it is clear that these accountsdisagreed with one another on significant points. These four pointswould already make the problem of determining**Pythagoras**’ philosophicalbeliefs more difficult than determining those of almost any otherancient philosopher, but a fifth factor complicates matters evenmore. By the third century CE, when the first detailed accounts of**Pythagoras**that survive intact were written,**Pythagoras**had come t...2.2 Post-Aristotelian Sources for

**Pythagoras**The problems regarding the sources for the life and philosophy of

**Pythagoras**are quite complicated, but it is impossible to understandthe Pythagorean Question without an accurate appreciation of at leastthe general nature of these problems. It is best to start with theextensive but problematic later evidence and work back to the earlierreliable evidence. The most detailed, extended and hence mostinfluential accounts of**Pythagoras**’ life and thought date to the thirdcentury CE, some 800 years af...2.3 Plato and Aristotle as Sources for

**Pythagoras**In reconstructing the thought of early Greek philosophers, scholarsoften turn to Aristotle’s and Plato’s accounts of their predecessors,although Plato’s accounts are embedded in the literary structure ofhis dialogues and thus do not pretend to historical accuracy, whileAristotle’s apparently more historical presentation masks aconsiderable amount of reinterpretation of his predecessors’ views interms of his own thought. In the case of

**Pythagoras**, what is strikingis the essential agreement of...References to

**Pythagoras**by Xenophanes (ca. 570–475 BCE) andHeraclitus (fl. ca. 500 BCE) show that he was a famous figure in thelate sixth and early fifth centuries. For the details of his life wehave to rely on fourth-century sources such as Aristoxenus,Dicaearchus and Timaeus of Tauromenium. There is a great deal ofcontroversy about his origin and early life, but there is agreementthat he grew up on the island of Samos, near the birthplace of Greekphilosophy, Miletus, on the coast of Asia Minor. There are a number ofreports that he traveled widely in the Near East while living onSamos, e.g., to Babylonia, Phoenicia and Egypt. To some extent reportsof these trips are an attempt to claim the ancient wisdom of the eastfor**Pythagoras**and some scholars totally reject them (Zhmud 2012,83–91), but relatively early sources such as Herodotus (II. 81) andIsocrates (Busiris 28) associate**Pythagoras**with Egypt, sothat a trip there seems quite plausible. Aristoxenus says that he leftSamos at t...One of the manifestations of the attempt to glorify

**Pythagoras**in thelater tradition is the report that he, in fact, invented the wordphilosophy. This story goes back to the early Academy, since it isfirst found in Heraclides of Pontus (Cicero, Tusc. V 3.8;Diogenes Laertius, Proem). The historical accuracy of thestory is called into question by its appearance not in a historical orbiographical text but rather in a dialogue that recounted Empedocles’revival of a woman who had stopped breathing. Moreover, the storydepends on a conception of a philosopher as having no knowledge butbeing situated between ignorance and knowledge and striving forknowledge. Such a conception is thoroughly Platonic, however (see,e.g., Symposium204A), and Burkert demonstrated that it couldnot belong to the historical**Pythagoras**(1960). For a recent attemptto defend at least the partial accuracy of the story, see Riedweg2005: 90–97 and the response by Huffman 2008a:207–208; seealso Zhmud 2012a, 428–430. Even...In the modern world

**Pythagoras**is most of all famous as amathematician, because of the theorem named after him, and secondarilyas a cosmologist, because of the striking view of a universe ascribedto him in the later tradition, in which the heavenly bodies produce“the music of the spheres” by their movements. It shouldbe clear from the discussion above that, while the early evidenceshows that**Pythagoras**was indeed one of the most famous early Greekthinkers, there is no indication in that evidence that his fame wasprimarily based on mathematics or cosmology. Neither Plato norAristotle treats**Pythagoras**as having contributed to the developmentof Presocratic cosmology, although Aristotle in particular discussesthe topic in some detail in the first book of the Metaphysicsand elsewhere. Aristotle evidently knows of no cosmology of**Pythagoras**that antedates the cosmological system of the “so-calledPythagoreans,” which he dates to the middle of the fifthcentury, and which is found in the fra...- Life & Works
- Pythagorean Beliefs
- Pythagoras & Plato
- Conclusion

What is known of

**Pythagoras**comes from later writers piecing together fragments of his life from contemporaries and students. It is known that**Pythagoras**was born on the island of Samos, off Asia Minor, where his ancestors had settled after leaving Phlius, a city in the northwest Peloponnese, after the civil war there in 380 BCE. He received a quality education as his father, Mnesarchus, was a wealthy merchant. He may have studied in Babylon and in Egypt and possibly had the best Greek tutors...As noted, none of

**Pythagoras**’ writings – if he wrote anything – have survived and, owing to the secrecy he demanded of his students, the specifics of his teachings were carefully kept. The philosopher Porphyry (l. c. 234 - c. 305 CE), who wrote a later biography of**Pythagoras**, noted:The Greek historian Herodotus (l.c. 484 - c. 425/413 BCE) alludes to**Pythagoras**(though famously refuses to name him) in his Histories:Like the Pythagorean Theorem,**Pythagoras**’ concept of the transmigration of sou...It is possible that Plato began as a student of Socrates, adhering to dialectic in establishing truth, and then only gradually moved toward embracing the idealism of

**Pythagoras**– as some scholars have claimed – but it seems more probable that Socrates himself was aligned with Pythagorean thought. There is really no way of establishing any claim along these lines since most of what we know of Socrates comes from Plato’s Dialogues which were written after Socrates’ death when Plato was already...The Phaedo also establishes the geography of the afterlife which would later be used by the Church in creating the concepts of Hell, Purgatory, and Heaven. The concept of purgatory first appears in Phaedo 108b-d, judgment of the dead in 113d-e, Hell in 113e-114a, and heaven in 109d-110b. Plato’s argument for an ultimate, undeniable, realm of truth, from which all other truths are established, is also evident in the gospel narratives of the Bible, most notably the Gospel of John, and in the ep...

- Joshua J. Mark

Pythagoras (c. 570—c. 495 B.C.E) The

**pre-Socratic Greek philosopher**Pythagoras must have been one of the world’s greatest persons, but he wrote nothing, and it is hard to say how much of the doctrine we know as Pythagorean is due to the founder of the society and how much is later development.Pythagoras was born in about

**570 BC on the Greek island of Samos.**His father was a merchant. Pythagoras was taught mathematics by Thales, who brought mathematics to the Greeks from Ancient Egypt, and by Anaximander, who was an earlier student of Thales. Thales advised Pythagoras to visit Egypt, which he did when he was about 22 years old.**Greek**philosopher, scientist, and religious scholar The Greek philosopher, scientist, and religious teacher Pythagoras developed a school of thought that accepted the passage of the soul into another body and established many influential mathematical and philosophical theories.Jul 09, 2020 · Pythagoras is

**perhaps the most famous figure in the group of ancient Greek philosophers known as the Pre-Socratics.**This is largely due to the Pythagorean Theorem, a mathematical theorem that is still widely used today. Apart from being a mathematician, Pythagoras was also an influential thinker in other areas.- Dhwty

- Why Is This Useful?
- How Do I Use It?
- and You Can Prove The Theorem Yourself !
- another, Amazingly Simple, Proof

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!)

Write it down as an equation: Then we use algebrato find any missing value, as in these examples: You can also read about Squares and Square Roots to find out why √169 = 13 It works the other way around, too: when the three sides of a triangle make a2 + b2 = c2, then the triangle is right angled.

Get paper pen and scissors, then using the following animation as a guide: 1. Draw a right angled triangle on the paper, leaving plenty of space. 2. Draw a square along the hypotenuse (the longest side) 3. Draw the same sized square on the other side of the hypotenuse 4. Draw lines as shown on the animation, like this: 5. Cut out the shapes 6. Arrange them so that you can prove that the big square has the same area as the two squares on the other sides

Here is one of the oldest proofs that the square on the long side has the same area as the other squares. Watch the animation, and pay attention when the triangles start sliding around. You may want to watch the animation a few times to understand what is happening. The purple triangle is the important one. We also have a proof by adding up the areas.

01 Pythagoras was

**a mathematician and philosopher from**Ancient Greece. 02 Around 570 BC, Pythagoras was born on Samos, a Greek Island. 03 He was the son of a seal engraver named Mnesarchus. 04 The cause of his death around 496 BC remains to be a mystery.

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