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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.
Musica universalis. The musica universalis (literally universal music), also called music of the spheres or harmony of the spheres, is a philosophical concept that regards proportions in the movements of celestial bodies —the Sun, Moon, and planets —as a form of music. The theory, originating in ancient Greece, was a tenet of Pythagoreanism ...
The Golden Verses Of Pythagoras And Other Pythagorean Fragments. Theosophical Publishing House. Joost-Gaugier, Christiane L. (2007). Measuring Heaven: Pythagoras and his Influence on Thought and Art in Antiquity and the Middle Ages. Cornell University Press. ISBN 978-0-8014-7409-5; Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A ...
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. [38] This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3.
Viète. de Moivre. Euler. Fourier. v. t. e. In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.
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.
The album Numbers, subtitled "A Pythagorean Theory Tale," was based on a fictional planet in a far-off galaxy named Polygor. The album included a booklet with excerpts from a planned book of the same name written by Chris Bryant and Allan Scott. The booklet features pen-and-ink illustrations drawn by Stevens. [2]
Comparison of equal-tempered (black) and Pythagorean (green) intervals showing the relationship between frequency ratio and the intervals' values, in cents. Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths [2] which are "pure" or perfect, with ratio .