By Donald C. Benson
Книга A Smoother Pebble: Mathematical Explorations A Smoother Pebble: Mathematical Explorations Книги Математика Автор: Donald C. Benson Год издания: 2003 Формат: pdf Издат.:Oxford college Press Страниц: 280 Размер: 11,1 ISBN: 0195144368 Язык: Английский0 (голосов: zero) Оценка:This e-book takes a unique examine the themes of college mathematics--arithmetic, geometry, algebra, and calculus. during this walk at the mathematical beach we are hoping to discover, quoting Newton, "...a smoother pebble or a prettier shell than ordinary..." This booklet assembles a set ofmathematical pebbles which are vital in addition to appealing.
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Extra info for A Smoother Pebble: Mathematical Explorations
With permission, Acoustical Society of America, Copyright 1965. The Music of the Ratios 47 of the beats is equal to the difference in the frequencies of the two tones. The addition of the second tone does not increase our sense of loudness. Beats occur because the two tones alternately reinforce and cancel each other—that is, they are alternately in and out of phase. 10 shows the pressure-time graph of an instance of beats. 3. Two tones can be too close together to be heard as separate tones and too far apart to be heard as beats.
The addition of two like magnitudes. The sum of two geometric magnitudes is the magnitude of a geometric figure consisting of the two underlying figures side by side. 2. The multiplication of a magnitude by a natural number. Definition 4 implies that each multiple of a magnitude—double, triple, or any integral multiple—is also a magnitude of the same kind. In other words, if A is a geometric magnitude and n is a natural number, it makes sense to speak of the magnitude nA, the n-fold multiple of A.
1 shows a hypothetical instrument that would be especially suitable for the Pythagorean experiments. Although no one knows how ancient Greek music actually sounded, we do know that the Pythagoreans made a connection between music and mathematics. The Pythagoreans discovered that harmonious musical intervals are generated by pairs of string lengths with simple numerical ratios. These intervals are called Pythagorean to distinguish them from the slightly different equal-tempered intervals in current musical use.
A Smoother Pebble: Mathematical Explorations by Donald C. Benson