- 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 – c. 495 BC) was an ancient Ionian Greek philosopher and the eponymous 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.
- The Pythagorean Question
- 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 ofPythagoras 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 ofPythagoras 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 Pythagorasthat antedates the cosmological system of the “so-calledPythagoreans,” which he dates to the middle of the fifthcentury, and which is found in the fra...
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 mathematics and Western rational philosophy.
May 23, 2019 · Pythagoras (l.c. 571- c. 497 BCE) was a Greek philosopher whose teachings emphasized the immortality and transmigration of the soul (reincarnation), virtuous, humane behavior toward all living things, and the concept of “number” as truth in that mathematics not only cleared the mind but allowed for an objective comprehension of reality.
- Joshua J. Mark
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.
Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it. View eleven larger pictures
- 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.
Pythagoras (fl 580-500, BC) was born in Samos on the western coast of what is now Turkey. He was reportedly the son of a substantial citizen, Mnesarchos. There he lived for many years under the rule of the tyrant Polycrates, who had a tendency to switch alliances in times of conflict -- which were frequent.
Nov 26, 2019 · 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.