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Pythagoras of Samos[ a] ( Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC) [ b] was an ancient Ionian Greek philosopher, polymath 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, the West in general.
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle ) is equal to the sum of the areas of the squares on the other two sides.
Pythagoras' teachings and Pythagoreanism influenced Plato's writings on physical cosmology, psychology, ethics and political philosophy in the 5th century BC. However, Plato adhered to the dominant Greek philosophy, and the Platonic philosophy suppressed the combination of experimental method and mathematics which was an inherent part of ...
Pythagorean trigonometric identity. The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions. The identity is.
Fyodor Bronnikov, Pythagoreans' Hymn to the Rising Sun, 1869. [1] Oil on canvas. The Golden Verses ( Greek: ἔπη χρυσᾶ or χρύσεα ἔπη, Chrysea Epē [kʰrýsea épɛː]; Latin: Aurea Carmina) are a collection of moral exhortations comprising 71 lines written in dactylic hexameter. They are traditionally attributed to the ...
Pythagorean astronomical system. An astronomical system positing that the Earth, Moon, Sun, and planets revolve around an unseen " Central Fire " was developed in the fifth century BC and has been attributed to the Pythagorean philosopher Philolaus. [ 1][ 2] The system has been called "the first coherent system in which celestial bodies move in ...
Pythagoras rushed into the blacksmith shop to discover why, and found that the explanation was in the weight ratios. The hammers weighed 12, 9, 8, and 6 pounds respectively. Hammers A and D were in a ratio of 2:1, which is the ratio of the octave. Hammers B and C weighed 8 and 9 pounds.
Nicomachus of Gerasa says that they were "acknowledged by all the ancients, Pythagoras, Plato and Aristotle." Their earliest known use is a fragment of the Pythagorean philosopher Archytas of Tarentum: There are three means in music: one is arithmetic, second is the geometric, third is sub-contrary, which they call harmonic.