# when least is best how mathematicians discovered many clever ways to make things as small or as large as possible

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## When Least Is Best

**Author :**Paul J. Nahin

**ISBN :**9781400841363

**Genre :**Mathematics

**File Size :**28. 27 MB

**Format :**PDF, ePub, Docs

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What is the best way to photograph a speeding bullet? Why does light move through glass in the least amount of time possible? How can lost hikers find their way out of a forest? What will rainbows look like in the future? Why do soap bubbles have a shape that gives them the least area? By combining the mathematical history of extrema with contemporary examples, Paul J. Nahin answers these intriguing questions and more in this engaging and witty volume. He shows how life often works at the extremes--with values becoming as small (or as large) as possible--and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima. From medieval writings to the development of modern calculus to the current field of optimization, Nahin tells the story of Dido's problem, Fermat and Descartes, Torricelli, Bishop Berkeley, Goldschmidt, and more. Along the way, he explores how to build the shortest bridge possible between two towns, how to shop for garbage bags, how to vary speed during a race, and how to make the perfect basketball shot. Written in a conversational tone and requiring only an early undergraduate level of mathematical knowledge, When Least Is Best is full of fascinating examples and ready-to-try-at-home experiments. This is the first book on optimization written for a wide audience, and math enthusiasts of all backgrounds will delight in its lively topics.

## Inside Your Calculator

**Author :**Gerald R. Rising

**ISBN :**0470124598

**Genre :**Mathematics

**File Size :**77. 14 MB

**Format :**PDF, Kindle

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Uncover the mysteries that lie within your calculator This remarkable book explores the simple internal calculator processes—algorithms and programs—that tell us, for example, that the cosine of 56? is 0.5591929035. Using carefully constructed diagrams and figures, the author effectively demonstrates how calculator keys compute powers, roots, logarithms, and trigonometry functions, while also providing insights into simple programming, the conversion between decimal and binary numeration, and perhaps most importantly, the structure of our numeration systems. Many people believe that the processes that drive calculators demand advanced mathematical concepts; however, this book proves that a minimal understanding of algebra and geometry is all that is needed to follow the step-by-step explanations of how scientific calculators work. Inside Your Calculator: From Simple Programs to Significant Insights is a complete and multifaceted exercise in critical thinking. This book features: A detailed explanation of how to use a graphics calculator and program basic functions A discussion of the history of mathematics when appropriate, which provides a foundation for further learning Fundamental mathematical lessons and interesting applications of pre-calculus mathematics A thorough review of the fundamentals of programming, algebra, and geometry needed to gain insight into why the algorithms work and how the results are meaningful in our lives While the simultaneous use of a calculator is not needed to gain insight into how the algorithms work, those who do have a programmable graphics calculator can experiment with the programs presented in the book. These programs may be used on TI-84 and TI-83 calculators, and additional information for other Texas Instruments calculators as well as the Casio FX series is available on the book's related web site. As a result of over fifty years of award-winning teaching experience in both high school and college classrooms, Dr. Rising anticipates and answers potential questions from readers, and he successfully brings this subject alive in an illuminating and entertaining way. This book is therefore not only ideal for undergraduate mathematics majors as either a primary or supplemental text, but it also appeals to anyone with an interest in mathematics and its ideas. View Dr. Rising's book presentation: http://www.youtube.com/watch?v=aqadHbc2YOA

## Mathematics And Scientific Representation

**Author :**Christopher Pincock

**ISBN :**9780199921096

**Genre :**Philosophy

**File Size :**80. 71 MB

**Format :**PDF

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Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a scientific representation. Several different sorts of contributions from mathematics are then articulated. Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge. In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument for mathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of its interpretation and epistemology. Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics.

## Dr Euler S Fabulous Formula

**Author :**Paul J. Nahin

**ISBN :**0691118221

**Genre :**Mathematics

**File Size :**64. 9 MB

**Format :**PDF, Kindle

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Accessible to any reader with the equivalent of the first two years of college mathematics, this is the story behind one of the world's most influential mathematical equations. 2 halftones. 77 line illustrations.

## Mathematical Reviews

**Author :**

**ISBN :**UOM:39015059777667

**Genre :**Mathematics

**File Size :**40. 3 MB

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## Mrs Perkins S Electric Quilt

**Author :**Paul J. Nahin

**ISBN :**1400833469

**Genre :**Mathematics

**File Size :**79. 53 MB

**Format :**PDF, ePub, Docs

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What does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins's Electric Quilt. With his trademark combination of intriguing mathematical problems and the historical anecdotes surrounding them, Nahin invites readers on an exciting and informative exploration of some of the many ways math and physics combine to create something vastly more powerful, useful, and interesting than either is by itself. In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. Each chapter includes problems--some three dozen in all--that challenge readers to try their hand at applying what they have learned. Just as in his other books of mathematical puzzles, Nahin discusses the historical background of each problem, gives many examples, includes MATLAB codes, and provides complete and detailed solutions at the end. Mrs. Perkins's Electric Quilt will appeal to students interested in new math and physics applications, teachers looking for unusual examples to use in class--and anyone who enjoys popular math books.

## Great Feuds In Mathematics

**Author :**Hal Hellman

**ISBN :**STANFORD:36105114410231

**Genre :**Mathematics

**File Size :**54. 22 MB

**Format :**PDF, ePub

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Praise for Hal Hellman Great Feuds in Mathematics "Those who think that mathematicians are cold, mechanical proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man. But Hellman's stories also show how scientific fights bring out sharper formulations and better arguments." -Professor Dirk van Dalen, Philosophy Department, Utrecht University Great Feuds in Technology "There's nothing like a good feud to grab your attention. And when it comes to describing the battle, Hal Hellman is a master." -New Scientist Great Feuds in Science "Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences." -American Scientist "Hellman has assembled a series of entertaining tales . . . many fine examples of heady invective without parallel in our time." -Nature Great Feuds in Medicine "This engaging book documents [the] reactions in ten of the most heated controversies and rivalries in medical history. . . . The disputes detailed are . . . fascinating. . . . It is delicious stuff here." -The New York Times "Stimulating." -Journal of the American Medical Association

## Science Year

**Author :**

**ISBN :**UCSD:31822033645375

**Genre :**Science

**File Size :**73. 73 MB

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## Choice

**Author :**

**ISBN :**STANFORD:36105122345049

**Genre :**Academic libraries

**File Size :**64. 37 MB

**Format :**PDF, ePub, Mobi

**Download :**418

**Read :**675

## The Journal Of The Indian Academy Of Mathematics

**Author :**Indian Academy of Mathematics

**ISBN :**UOM:39015072599270

**Genre :**Mathematics

**File Size :**47. 66 MB

**Format :**PDF, Docs

**Download :**443

**Read :**1057