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 ebook takes a unique examine the subjects of faculty 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 suite ofmathematical pebbles which are very important in addition to attractive.
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Extra info for A Smoother Pebble: Mathematical Explorations
It is the timbre that tells us that we are hearing a violin and not a guitar. Integer multiples, two or greater, of a given frequency are called harmonics of that frequency. The string, woodwind, and brass instruments have harmonic partials. However, the drum, the xylophone, the bells, and most other percussion instruments have nonharmonic partials that are not integer multiples of a fundamental frequency. We will see in the discussion on psychoacoustics that the consonance of the Pythagorean intervals stems from the fact that the higher partial frequencies of a vibrating string are all harmonics of the fundamental.
BCE), Meno (translated by Benjamin Jowett) THE ANCIENT GREEKS EMBARKED HUMANITY on the Scientific VOVage of discovery that continues to the present day. The greatest of the Greek mathematical gifts to us from antiquity was the notion of proof. In this chapter, we look at certain fundamental accomplishments of rigorous Greek mathematical thought—two alternate developments of the theory of ratio and proportion, subtle methods of filling in the gaps between the whole numbers. Thereby the Greeks carried forward the development of the number system.
Were not all these answers given out of his own head? Meno: Yes, they were all his own. Socrates: And yet, as we were just now saying, he did not know? Meno: True. Socrates: But still he had in him those notions of his—had he not? Meno: Yes. Socrates: Then he who does not know may still have true notions of that which he does not know? Meno: He has. —PLATO (4277-347? BCE), Meno (translated by Benjamin Jowett) THE ANCIENT GREEKS EMBARKED HUMANITY on the Scientific VOVage of discovery that continues to the present day.