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A comprehensive and intriguing account of the evolution of arithmetic and geometry, trigonometry and algebra, explores the interconnections among mathematics, physics, and mathematical astronomy and provides a history of the discipline from a new perspective. Originally published as The Norton History of the Mathematical Sciences. Reprint.
Virtually every volume on mythology contains legends connected with the rainbow and practically all modern textbooks of physics include some exposition of the optical principles which account for the bow. Mankind has been thinking, talking and writing about the rainbow for thousands of years. The Rainbow: from Myth to Mathematics gathers material from a great number of primary and secondary sources in the hopes that readers may be tempted to study further some aspects of the history of the theory of the rainbow. Includes information on Aristotle, Francis Bacon, the Christian tradition, color, Rene, Descartes, fogbow, Augustin Fresnel, Galileo Galilei, halo, Islamic tradition, Jesuits, Johann Kepler, nature of light, mirrors, Sir Isaac Newton, Olympiodorus, physics, rainbow breadth, reflection, refraction, Robert Grosseteste, Themo Judoci, Witelo, etc.
This is an exploration of the development of mathematics, from the ancient to the modern world. It covers all the major aspects of the discipline - early geometry, the growth of calculus and mechanics, the development of algebra, and the interplay between mathematics and modern physics.
Presents the main ideas and current approaches in inquiry-based, content-rich mathematics education.
From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.
A. THE TEXT The main importance of these two treatises lies in the insight they provide into Spinoza's conception of the relation between mathematics and certain disciplines not touched upon elsewhere in his major writings. The mathematics they involve are not the as those of the Ethics however, and the precise connection same between the geometrical order of this work and these excursions into optics and probability is by no means obvious. Add to this difficulty the knotty problems presented by their editorial his tory, dating and scientific background, and it is not perhaps surprising that in spite of the fact that they provide such an excellent illustration of Spinoza's reaction to certain important developments in the history of physics and mathematics, they should not, so far, have attracted much attention. They were first published in 1687 by Levyn van Dyck (d. 1695), official printer to the town council in The Hague. Printing anything by Spinoza was not without its risks, and it is probably significant that during the same year van Dyck should also have published a lengthy and elaborate refutation of Spinozism by 1 the pious and eccentric physician ]. F. Helvetius. Spinoza's name was omitted from the title-page, possibly because the editor or publisher thought that his reputation as an atheist might prejudice the sale of the booklet, and it was not until 1860 that the Amsterdam bookseller Frederik Muller (1817-1881) identified him as its author.
Venerated as god and goddess, feared as demon and pestilence, trusted as battle omen, and used as a proving ground for optical theories, the rainbow's image is woven into the fabric of our past and present. From antiquity to the nineteenth century, the rainbow has played a vital role in both inspiring and testing new ideas about the physical world. Although scientists today understand the rainbow's underlying optics fairly well, its subtle variability in nature has yet to be fully explained. Throughout history the rainbow has been seen primarily as a symbol&—of peace, covenant, or divine sanction&—rather than as a natural phenomenon. Lee and Fraser discuss the role the rainbow has played in societies throughout the ages, contrasting its guises as a sign of optimism, bearer of Greek gods' messages of war and retribution, and a symbol of the Judeo-Christian bridge to the divine. The authors traverse the bridges between the rainbow's various roles as they explore its scientific, artistic, and folkloric visions. This unique book, exploring the rainbow from the perspectives of atmospheric optics, art history, color theory, and mythology, will inspire readers to gaze at the rainbow anew. For more information on The Rainbow Bridge, visit: &
All historians of mathematics and students of the field will want a copy of this remarkable resource on their bookshelves.
A collection of personal reminiscences of the part science has played in the author's life, and the almost coincidental "recurrences" that early life events have had to create directions in his career.

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