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Mathematics and Music: In Search of Harmony (part 9)

5. Mathematics in the Emergence of Temperament Temperament in the general sense means a scale in which all or almost all intervals are slightly inaccurate but undistorted. They end up valuing certain intervals over others, in the sense that the former correspond to the same frequency ratios as the others.
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Proportional Fourth

Given three rational numbers a, b, and nonzero, the fourth proportional of these numbers is called a number x such that: Example: Determine the fourth proportional of the numbers 8, 12, and 6. Solution: We indicate by x the fourth proportional and set the proportion. : (applying the fundamental property) 8. x = 12.
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Ascending function and decreasing function

Given a function f: A B, we say that f is increasing in some set A 'A if and only if, for any x 1 A' and x 2 A ', with x 1 2, we have f (x 1) 2). For example, the function f: IR IR defined by f (x) = x + 1 is increasing in IR because: x 1 2 => x 1 +1 2 +1 => f (x 1) 2) That is: When domain values ​​grow, so do your images.
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Tragic death of some mathematicians

Tales of Miletus - asphyxiated by the crowd when leaving a show. Archimedes - murdered by a Roman soldier. Eratosthenes - killed himself, starving himself. Hypatia - cut by a group of exalted people during a mutiny in Alexandria. Évariste Galois - killed in a duel. Pythagoras - assassinated in Tarento during a revolution.
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Working with gold material and logic blocks in the early grades

Karen Daltoé Sueli Strelow Maria Montessori Maria Montessori (1870-1952) was born in Italy. He became interested in the study of the sciences, but decided on medicine at the University of Rome. He directed his career to psychiatry and soon became interested in disabled children. “Maria Montessori's great contribution to modern pedagogy was the child's awareness”, realizing that they responded quickly and enthusiastically to the stimuli to perform tasks, exercising motor skills and experiencing autonomy.
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Seeing is believing… (II)

A mathematical argument undoes the creation of a real thing. The sequential nature of self-awareness immediately gives you natural numbers like glasses to see the reality of the world. Self-awareness cannot see the supposed reality of the world in any other way than sequentially. "Networks" are not visions of self-awareness, they are imaginations of visions, because visions are unitary, direct imaginations one at a time, and following natural numbers, although the imagination that all nodes of the network are real simultaneously does not offer obstacles to self-awareness.
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