The Pythagoreans presented as fact the dualism that life is controlled by opposite forces between Limited and Unlimited. It Pythagoras. Reproduced by permission of the Corbis Corporation. His study of musical intervals, leading to the discovery that the chief intervals can be expressed in numerical ratios relationships between numbers between the first four integers positive whole numbers , also led to the theory that the number ten, the sum of the first four integers, embraced the whole nature of number.
Pythagoras may have discovered the theorem which still bears his name in right triangles [triangle with one angle equal to 90 degrees], the square on the hypotenuse equals the sum of the squares on the other sides , although this proposal has been discovered on a writing stone dating from the time of the Babylonian king Hammurabi died c. Regardless of their sources, the Pythagoreans did important work in extending the body of mathematical knowledge. As a more general outline, the Pythagoreans presented the two contraries opposites , Limited and Unlimited, as ultimate principles, or truths.
Numerical oddness and evenness are equated with Limited and Unlimited, as are one and plurality many , right and left, male and female, motionlessness and movement, straight and crooked, light and darkness, and good and bad. It is not clear whether an ultimate One, or Monad, was presented as the cause of the two categories. The Pythagoreans, as a result of their religious beliefs and careful study of mathematics, developed a cosmology dealing with the structures of the universe which differed in some important respects from the world views at the time, the most important of which was their view of the Earth as a sphere which circled the center of the universe.
It is not known how much of this theory was credited to Pythagoras himself. The mathematical knowledge carried out by Pythagoras and his followers would have been enough to make him an important figure in the history of Western thought. However, his religious sect and the self-discipline and dedication which he taught, embracing as it did a vast number of ancient beliefs, make him one of the great teachers of religion in the ancient Greek world.
By the middle of the fourth century BCE, the Pythagoreans as a distinct group no longer existed. Though the group dispersed, the teachings of Pythagoras and much subsequent work have been attributed to his name. Because of the secrecy shrouding the beliefs of the brotherhood, it is not possible to accurately say which works are directly attributed to the philosopher and what were developed by his disciples. A man named Philolaus was one of his more eminent students and published Pythagorean views for the general public.
One account states that Pythagoras claimed to have lived previous lives and he could recall them in detail. Pythagoras was interested in the study of sound and musical instruments, a field of study for him that was closely tied to numerology and the cosmos.
He noticed that the shorter the string on a stringed musical instrument, such as a lyre, the higher the pitch it would produce. He recognized that a string that was twice as long emitted a sound that was an octave lower. If the ratio of the length of the strings was three to two, the musical interval produced was a fifth. When the ratio was four to three, the interval called a fourth was produced. Additionally, he determined that the pitch of the sound became higher as the tension on the string increased.
Many of his observations of sound and music are still relevant today. Pythagorean astronomy seems to have its roots in Babylon, which was where he presumably gained exposure to the subject during his early travels. The theories developed by Anaximander of Miletus, who was said to be his teacher, also influenced his views on the cosmos.
He used his concept of musical intervals to determine the position of the planets in relation to the position of Earth. Based on his theory, the order of the planets in increasing distance from Earth is: Moon, Mercury, Venus, the Sun, Jupiter, and Saturn.
The theory was later refined by placing Mercury and Venus above the Sun, since no solar transits of the planets had been observed. Using the perceived link to the orbits of the planets and musical intervals and the seven strings of the lyre, the Pythagoreans thought as the planets moved throughout the firmament they produced a celestial harmony called the music of the spheres.
Supposedly, only Pythagoras could hear the music coming from the planets; common people could not hear it because they had grown accustomed to the sound. To satisfy the Pythagorean idea of beauty, the stars must accordingly move in the simplest of curves, which is the circle. This idea of circular orbits for planets permeated astronomy until Johannes Kepler showed in the seventeenth century that the planets move in elliptical orbits.
The Pythagoreans did not believe in a flat Earth; rather, they adopted the notion of a spherical Earth. Their view of the solar system was that the Earth moves around an unseen central fire every 24 hours. The central fire cannot be seen because another object, a counter Earth, also rotates about the central fire every 24 hours and always remains between the Earth and the central fire.
According to Aristotle, the Pythagoreans were also able to explain the cycle of night and day using this model. The members sought the number associated with a specific person or animal. As an example, for a horse they associated the number of small stones needed to outline a horse, thus this became the number of the horse. Konon ia juga adalah orang pertama yang menyebut dirinya sebagai filsuf "pecinta kebijaksanaan" dan membagi dunia menjadi lima zona iklim.
Namun, para ahli sejarah klasik masih memperdebatkan apakah Pythagoras benar-benar telah membuat temuan-temuan ini, dan banyak pencapaian yang dikaitkan dengan namanya mungkin sudah ada sebelumnya atau dicetuskan oleh rekan atau penerusnya. Selain itu, masih diperdebatkan apakah ia benar-benar telah bersumbangsih terhadap bidang matematika atau filsafat alam.
Pemikiran Pythagoras memengaruhi Plato, dan dialog-dialog karya Plato khususnya Timaios menunjukkan pengaruh dari ajaran pythagoreanisme.
Gagasan pythagoreanisme mengenai kesempurnaan matematis juga berdampak terhadap seni Yunani Kuno. Ajaran pythagoreanisme kembali bangkit pada abad pertama SM di kalangan penganut platonisme pertengahan, yang beriringan dengan kemunculan neopythagoreanisme.
Pythagoras terus dianggap sebagai seorang filsuf ulung pada Abad Pertengahan, dan filsafatnya sangat berpengaruh terhadap ilmuwan seperti Nicolaus Copernicus, Johannes Kepler, dan Isaac Newton.
Simbolisme pythagoreanisme juga digunakan oleh para pengamal esoterisme Barat modern, dan ajarannya seperti yang dirincikan dalam Metamorphoses karya penyair zaman Romawi Ovidius telah memengaruhi gerakan vegetarian modern. Rond v. Vanwege moeilijkheden met de stedelingen verhuisde hij uiteindelijk naar Metapontum, waar hij overleed.
Hij stond bekend als een filosofische en religieuze hervormer, maar onderzoekers leggen nu eens de nadruk op Pythagoras' wiskunde en filosofie, dan weer op zijn sjamanistische allure. Il suo pensiero ha avuto enorme importanza per lo sviluppo della scienza occidentale, avendo per primo intuito l'efficacia della matematica per descrivere il mondo. Le sue dottrine segnerebbero la nascita di una riflessione improntata all'amore per la conoscenza.
La scuola a lui intitolata fu il crogiolo nel cui ambito si svilupparono molte conoscenze, in particolare quelle matematiche e le sue applicazioni, come il noto teorema di Pitagora. Em a.
Cerca de a. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Pythagoras also related music to mathematics. He had long played the seven string lyre, and learned how harmonious the vibrating strings sounded when the lengths of the strings were proportional to whole numbers, such as , , Pythagoreans also realized that this knowledge could be applied to other musical instruments.
The reports of Pythagoras' death are varied. He is said to have been killed by an angry mob, to have been caught up in a war between the Agrigentum and the Syracusans and killed by the Syracusans, or been burned out of his school in Crotona and then went to Metapontum where he starved himself to death.
At least two of the stories include a scene where Pythagoras refuses to trample a crop of bean plants in order to escape, and because of this, he is caught. The Pythagorean Theorem is a cornerstone of mathematics, and continues to be so interesting to mathematicians that there are more than different proofs of the theorem, including an original proof by President Garfield. Home Contact About Subject Index.
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