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Pythagoras and the Ratios by Julie Ellis,Phyllis Hornung Peacock Pdf
Julie Ellis and Phyllis Hornung Peacock team up once again to explore Pythagorean ratios in this humorous sequel to WHAT'S YOUR ANGLE, PYTHAGORAS? Pythagoras and his cousins want to win a music contest, but first they must figure out how to play their instruments in tune, something that's never been done before. While trying to fix the problem, Pythagoras makes an important discovery--notes that sound pleasant together have a certain mathematical relationship. When Pythagoras applies this ratio to his cousins' pipes and lyres, the result is music to the ears.
Uses a story format to introduce the Pythagorean theorem. An ancient Greek boy, Pythagoras, helps his cousins produce pleasant music when he adjusts the mathematical ratios between the part of their pipes and lyres, knowledge he would later use to become a famous philosopher. Includes historical note. Suggested level: primary.
What's Your Angle, Pythagoras? by Judy Ellis,Julie Ellis Pdf
In ancient Greece, young Pythagoras discovers a special number pattern (the Pythagorean theorem) and uses it to solve problems involving right triangles.
Pythagoras by Louis C. Coakley,Dimitra Karamanides Pdf
Though known today primarily for the mathematical theorem that bears his name, Pythagoras was a mystically-minded philosopher with a particular interest in music, astronomy, cosmology, numerology, and the soul. This book paints a vivid picture of the world in which Pythagoras lived—and since the philosopher was so widely travelled that includes Greek, Egyptian, and Babylonian civilization in the sixth century BCE. Along with chapters discussing Pythagoras’s life and beliefs, as well as the lifestyle he advocated, there is a timeline listing important events from his life.
Pythagoras and the Early Pythagoreans by Leonid Zhmud Pdf
In ancient tradition, Pythagoras emerges as a wise teacher, an outstanding mathematician, an influential politician, and as a religious and ethical reformer. This volume offers a comprehensive study of Pythagoras, Pythagoreanism, and the early Pythagoreans through an analysis of the many representations of the individual and his followers.
This is the story of Pythagoras and the Pythagoreans, whose insights transformed the ancient world and still inspire the realms of science, mathematics, philosophy and the arts. Einstein said that the most incredible thing about our universe was that it was comprehensible at all. As Kitty Ferguson explains, Pythagoras had much the same idea - but 2,500 years earlier. Though known by many only for his famous Theorem, in fact the pillars of our scientific tradition - belief that the universe is rational, that there is unity to all things, and that numbers and mathematics are a powerful guide to truth about nature and the cosmos - hark back to the convictions of this legendary scholar. Kitty Ferguson brilliantly evokes Pythagoras' ancient world of, showing how ideas spread in antiquity, and chronicles the incredible influence he and his followers have had on so many extraordinary people in the history of Western thought and science. 'Pythagoras' influence on the ideas, and therefore on the destiny, of the human race was probably greater than that of any single man before or after him' - Arthur Koestler.
Pythagoras and the Doctrine of Transmigration by James Luchte Pdf
The mythical narrative of transmigration tells the story of myriad wandering souls, each migrating from body to body along a path of recurrence amid the becoming of the All. In this highly original study, James Luchte explores the ways in which the concept of transmigration is a central motif in Pythagoras' philosophy, representing its fundamental meaning. Luchte argues that the many strands of the tale of transmigration come together in the Pythagorean philosophical movement, revealing a unity in which, for Pythagoreans, existence and eschatology are separated only by forgetfulness. Such an interpretation that seeks to retrieve the unity of Pythagorean thought goes against the grain of a long-standing tradition of interpretation that projects upon Pythagoras the segregation of 'mysticism' and 'science'. Luchte lays out an alternative interpretation of Pythagorean philosophy as magical in the sense that it orchestrates a holistic harmonization of theoria and praxis and through this reading discloses the radical character of Pythagorean philosophy.
Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.
The Life and Times of Pythagoras by Susan Sales Harkins,William H. Harkins Pdf
Pythagoras was a man of his time—and for all time. So important to mankind was his birth that the gods sent his birth announcement via the Pythian oracle. Tradition holds that he studied with the greatest minds the ancients had to offer. Pherecydes taught him that the soul is immortal. Thales and Anaximander taught him to trust only what he experienced. He studied with the first recorded scientist. Egyptian priests taught him radical ideas about the human soul. From the Babylonians’ magi, he learned higher mathematics and about the cosmos. He probably had the most well rounded higher education of any other living person of his time, but when most men were done with life, Pythagoras was just making his mark. Around the age of fifty, he founded a school of higher mathematics, philosophy, music, and religion. His lessons still impact our scientific and moral communities today.
Brill's Companion to the Reception of Pythagoras and Pythagoreanism in the Middle Ages and the Renaissance by Irene Caiazzo,Constantinos Macris,Aurélien Robert Pdf
For the first time, the reader can have a synoptic view of the reception of Pythagoras and Pythagoreanism in the Middle Ages and the Renaissance, East and West, in a multicultural perspective. All the major themes of Pythagoreanism are addressed, from mathematics, number philosophy and metaphysics to ethics and religious thought.
Author : Robert Hahn Publisher : State University of New York Press Page : 301 pages File Size : 50,5 Mb Release : 2017-05-01 Category : Philosophy ISBN : 9781438464916
The Metaphysics of the Pythagorean Theorem by Robert Hahn Pdf
Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato's Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahn's book will enrich the study of ancient philosophy and mathematics alike.
