Pythagoras And The Ratios

Author: Julie Ellis
Editor: Charlesbridge
ISBN: 1607341891
File Size: 53,49 MB
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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.

Pythagoras Plato And The Golden Ratio

Author: Ken Wheeler
Editor:
ISBN: 9780971254152
File Size: 62,50 MB
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The Life And Times Of Pythagoras

Author: Susan Sales Harkins
Editor: Mitchell Lane Publishers, Inc.
ISBN: 1612288855
File Size: 30,27 MB
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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.

What S Your Angle Pythagoras

Author: Judy Ellis
Editor: Charlesbridge
ISBN: 1607341611
File Size: 23,10 MB
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In ancient Greece, young Pythagoras discovers a special number pattern (the Pythagorean theorem) and uses it to solve problems involving right triangles.

The World S Cyclopedia Of Science

Author:
Editor:
ISBN:
File Size: 31,37 MB
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Scientia Und Ars Im Hoch Und Sp Tmittelalter

Author: Ingrid Craemer-Ruegenberg
Editor:
ISBN:
File Size: 66,55 MB
Format: PDF
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Homage To Pythagoras

Author:
Editor:
ISBN:
File Size: 53,46 MB
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Music By The Numbers

Author: Eli Maor
Editor: Princeton University Press
ISBN: 0691202966
File Size: 35,24 MB
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How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century Music is filled with mathematical elements. The works of Bach are often said to possess a math-like logic, and Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen wrote music explicitly based on mathematical principles. Yet Eli Maor argues that it is music that has had the greater influence on mathematics, not the other way around. Starting with Pythagoras, proceeding through Schoenberg, and bringing the story up to the present with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who have played a role in the age-old relationship between music, mathematics, and the physical sciences. Weaving compelling stories of historical episodes with Maor's personal reflections as a mathematician and lover of classical music, this book will delight anyone who loves math and music.

The Music Of Pythagoras

Author: Kitty Ferguson
Editor: Bloomsbury Publishing USA
ISBN: 9780802779632
File Size: 67,90 MB
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The enthralling story of Pythagoras and the Pythagoreans, whose insights transformed the ancient world and still inspire the realms of science, mathematics, philosophy, and the arts. "Pythagoras's 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," wrote Arthur Koestler. Though most people know of him only for the famous Pythagorean Theorem (a2 +b2=c2), 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 sixth-century B.C. scholar. Born around 570 B.C. on the cultured Aegean island of Samos, Pythagoras (according to ancient tales) studied with the sage Thales nearby at Miletus, and with priests and scribes in Egypt and Babylon. Eventually he founded his own school at Croton in southern Italy, where he and his followers began to unravel the surprising deep truths concealed behind such ordinary tasks as tuning a lyre. While considering why some string lengths produced beautiful sounds and others discordant ones, they uncovered the ratios of musical harmony, and recognized that hidden behind the confusion and complexity of nature are patterns and orderly relationships. They had surprised the Creator at his drafting board and had glimpsed the mind of God! Some of them later would also find something darker in numbers and nature: irrationality, a revelation so unsettling and subversive that it may have contributed to the destruction of their brotherhood.

Transactions Of The Asiatic Society Of Japan

Author: Asiatic Society of Japan
Editor:
ISBN:
File Size: 77,89 MB
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List of transactions, v. 1-41 in v. 41.

Squaring The Circle

Author: Paul Calter
Editor: John Wiley & Sons Incorporated
ISBN:
File Size: 72,25 MB
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This truly unique new title should appeal to both mathematicians and mathematics educators. It should also find a small market among professional and reference book buyers: mathematical professionals with interest in travel, art, architecture. The title is intended for math students who are interested in art, or art students with an interest (or requirement) in mathematics, or professionals with interest in mathematics and art. Geometry concepts are introduced by analyzing well known buildings and works of art. The book is packaged with an access code which allows the reader into a protected site, which will contain most of the fine art from the book in full color as well as teaching resources. The text appeals both to mathematicians and to artists and will generally be used in courses that bridge the two subjects. --Publisher description.

Music

Author: Lisa Summer
Editor:
ISBN:
File Size: 18,24 MB
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Offers a critical look at New Age claims that music can be used to cure diseases, alleviate addictive behavior, and drive away harmful insects

Mechanics Heat Sound

Author: Lloyd William Taylor
Editor:
ISBN:
File Size: 12,22 MB
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Journal For The History Of Astronomy

Author:
Editor:
ISBN:
File Size: 66,64 MB
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A History Of Mathematics

Author: Jeff Suzuki
Editor: Pearson College Division
ISBN:
File Size: 79,88 MB
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For junior and senior level undergraduate courses, this text attempts to blend relevant mathematics and relevant history of mathematics, giving not only a description of the mathematics, but also explaining how it has been practiced through time.

Tonality In Western Culture

Author: Richard Norton
Editor: Penn State University Press
ISBN:
File Size: 53,86 MB
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This book initiates "the first critical appraisal of the whole of Western tonal consciousness, from the discoveries of Pythagoras to the latest popular song." While tonality has been unwittingly championed as the product of the bourgeois age in Europe and America from 1600 to 1900, Norton states, key-centered music is understood here merely to exhibit components of an encompassing sonic expressivity as durable as any language. The author analyzes fundamental components of Western tonal phenomena that have persisted in music from ancient Jewish cantillation to the so-called atonal procedures of the Schoenberg school and beyond. Norton isolates the role of traditional music theory in the creation of models that attempted to explain tonality solely in terms of the concretized and limited objectivity of the musical score. The author evaluates and discards those features of logical positivism, scientific empiricism, idealism, and vitalism that in his view have encumbered virtually all speculation on tonality. With this negation, his aim is to restore the composer as a creator subject to his own sonic object. The book's approach is particularly indebted to the thought of Theodor Adorno, the member of the Frankfurt School of critical theorists that Norton finds most capable of suggesting an authentic dialectic of tonality. The author interprets the activities of both theorists and composers from various periods within the context of their mutual and conflicting historical interests. Ranging through the fields of physics, acoustics, psychology, sociology, economics, and historical musicology and criticism, Norton demonstrates that the cognitive abilities and disabilities of humans as tonal hearers form a necessary ground for understanding the remarkable vitality of tonality as historical process. Current theories of human tonal activity are hopelessly limited, the book concludes, however self-preserving they have become through the sanction of academic respectability. In short, tonal science, as it is commonly practiced, is not tonal truth. In its place the author urges a thoroughgoing critique of the language and methodology of contemporary tonal speculation, an abandonment of its confining sphere of interest, and a new and liberating approach to tonal consciousness that incorporates all relevant data of human sonic cognition. This approach assumes that tonality is not merely the result of the physical unfolding of natural appearance--the overtone series that so enchanted Rameau, Schenker, Hindemith, and others--and the submission of composers to its assumed authority. Tonality is, rather, Norton contends, a decision made against the chaos of pitch and for the human potential to create works of music that speak with integrity and beauty, that as aesthetic creations neither lag behind nor rush ahead of human enjoyment and understanding.

What Is A Number

Author: Robert Tubbs
Editor: Johns Hopkins Univ Pr
ISBN:
File Size: 79,60 MB
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Mathematics often seems incomprehensible, a melee of strange symbols thrown down on a page. But while formulae, theorems, and proofs can involve highly complex concepts, the math becomes transparent when viewed as part of a bigger picture. What Is a Number? provides that picture. Robert Tubbs examines how mathematical concepts like number, geometric truth, infinity, and proof have been employed by artists, theologians, philosophers, writers, and cosmologists from ancient times to the modern era. Looking at a broad range of topics-from Pythagoras's exploration of the connection between harmonious sounds and mathematical ratios to the understanding of time in both Western and pre-Columbian thought-Tubbs ties together seemingly disparate ideas to demonstrate the relationship between the sometimes elusive thought of artists and philosophers and the concrete logic of mathematicians. He complements his textual arguments with diagrams and illustrations. This historic and thematic study refutes the received wisdom that mathematical concepts are esoteric and divorced from other intellectual pursuits-revealing them instead as dynamic and intrinsic to almost every human endeavor.