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A Dictionary of Real Numbers by Jonathan Borwein Pdf
How do we recognize that the number . 93371663 . . . is actually 2 IoglQ(e + 7r)/2 ? Gauss observed that the number 1. 85407467 . . . is (essentially) a rational value of an elliptic integral-an observation that was critical in the development of nineteenth century analysis. How do we decide that such a number is actually a special value of a familiar function without the tools Gauss had at his disposal, which were, presumably, phenomenal insight and a prodigious memory? Part of the answer, we hope, lies in this volume. This book is structured like a reverse telephone book, or more accurately, like a reverse handbook of special function values. It is a list of just over 100,000 eight-digit real numbers in the interval [0,1) that arise as the first eight digits of special values of familiar functions. It is designed for people, like ourselves, who encounter various numbers computationally and want to know if these numbers have some simple form. This is not a particularly well-defined endeavor-every eight-digit number is rational and this is not interesting. However, the chances of an eight digit number agreeing with a small rational, say with numerator and denominator less than twenty-five, is small. Thus the list is comprised primarily of special function evaluations at various algebraic and simple transcendental values. The exact numbers included are described below. Each entry consists of the first eight digits after the decimal point of the number in question.
Civil Disobedience: An Encyclopedic History of Dissidence in the United States by Mary Ellen Snodgrass Pdf
Throughout American history, people with strong beliefs that ran counter to society's rules and laws have used civil disobedience to advance their causes. From the Boston Tea Party in 1773, to the Pullman Strike in 1894, to the draft card burnings and sit-ins of more recent times, civil disobedience has been a powerful force for effecting change in American society.This comprehensive A-Z encyclopedia provides a wealth of information on people, places, actions, and events that defied the law to focus attention on an issue or cause. It covers the causes and actions of activists across the political spectrum from colonial times to the present, and includes political, social economic, environmental, and a myriad of other issues."Civil Disobedience" ties into all aspects of the American history curriculum, and is a rich source of material for essays and debates on critical issues and events that continue to influence our nation's laws and values. It explores the philosophies, themes, concepts, and practices of activist groups and individuals, as well as the legislation they influenced. It includes a detailed chronology of civil disobedience, listings of acts of conscience and civil disobedience by act and by location, a bibliography of primary and secondary sources, and a comprehensive index complete the set.
United States Army Infantry, Artillery, Armor/Cavalry Battalions 1957-2011 by Timothy S Aumiller Pdf
Every infantry, cavalry, armor, field artillery, and air defense artillery battalion in the US Army 1957-2011 is listed, together with its station through the period.
Catalogue de Timbres de France 2020-2021 by Spink Maury Pdf
The Spink Maury Catalogue has traditionally provided the highest level of detail for the stamps and covers of France and the French colonies, with thousands of top quality illustrations and prices updated every year. It was acquired by Spink in 2015, and the editors have since endeavoured to make this the premium reference work of its kind.
United States. Congress. House. Committee on Appropriations. Subcommittee on Departments of Labor, and Health, Education, and Welfare, and Related Agencies
Author : United States. Congress. House. Committee on Appropriations. Subcommittee on Departments of Labor, and Health, Education, and Welfare, and Related Agencies Publisher : Unknown Page : 1312 pages File Size : 48,7 Mb Release : 1972 Category : Electronic ISBN : LOC:00177245173
Departments of Labor and Health, Education, and Welfare Appropriations for 1973 by United States. Congress. House. Committee on Appropriations. Subcommittee on Departments of Labor, and Health, Education, and Welfare, and Related Agencies Pdf