In the early 17th century, both Jost Bürgi and John Napier dared to invent a logarithm table whose construction required tens of thousands of computing steps. These tables reduced computing effort for multiplication and division by an order of magnitude. Indeed, their invention launched a computing revolution that continues to this day. The book tells the story of Bürgi's and Napier's work, and how Henry Briggs built on Napier's idea, creating a table of logarithms that was easier to use. John Napier and Henry Briggs described their methods in detail; distribution of their results was widespread. In contrast, Jost Bürgi did not leave detailed records of his work. Just a few copies of his table and terse handwritten instructions for its use have survived. To fill this gap, the book reconstructs Bürgi's thinking leading up to his table. The reader looks over his shoulder, so to speak, and learns how Bürgi came upon the idea, how he decided on the specific format of the table, and how his instructions should be interpreted. And so the reader experiences the magic of the invention of logarithms. The final chapters examine the question "Who invented logarithms?". For centuries, few people were aware of Bürgi's work; John Napier was considered to be the sole inventor. This changed at the middle of the 19th century when Jost Bürgi's work became more widely known. Since then there has been extensive debate whether Bürgi should be considered an independent co-inventor. Careful parsing of the history of logarithm going back to Archimedes of antiquity then reveals that, without doubt, John Napier and Jost Bürgi are independent co-inventors of logarithms.

With over 6,000 entries, CRC Standard Mathematical Tables and Formulae, 32nd Edition continues to provide essential formulas, tables, figures, and descriptions, including many diagrams, group tables, and integrals not available online. This new edition incorporates important topics that are unfamiliar to some readers, such as visual proofs and sequences, and illustrates how mathematical information is interpreted. Material is presented in a multisectional format, with each section containing a valuable collection of fundamental tabular and expository reference material. New to the 32nd Edition A new chapter on Mathematical Formulae from the Sciences that contains the most important formulae from a variety of fields, including acoustics, astrophysics, epidemiology, finance, statistical mechanics, and thermodynamics New material on contingency tables, estimators, process capability, runs test, and sample sizes New material on cellular automata, knot theory, music, quaternions, and rational trigonometry Updated and more streamlined tables Retaining the successful format of previous editions, this comprehensive handbook remains an invaluable reference for professionals and students in mathematical and scientific fields.

The oldest known mathematical table was found in the ancient Sumerian city of Shuruppag in southern Iraq. Since then, tables have been an important feature of mathematical activity; table making and printed tabular matter are important precursors to modern computing and information processing. This book contains a series of articles summarising the technical, institutional and intellectual history of mathematical tables from earliest times until the late twentieth century. It covers mathematical tables (the most important computing aid for several hundred years until the 1960s), data tables (eg. Census tables), professional tables (eg. insurance tables), and spreadsheets - the most recent tabular innovation. The book is presented in a scholarly yet accessible way, making appropriate use of text boxes and illustrations. Each chapter has a frontispiece featuring a table along with a small illustration of the source where the table was first displayed. Most chapters have sidebars telling a short "story" or history relating to the chapter. The aim of this edited volume is to capture the history of tables through eleven chapters written by subject specialists. The contributors describe the various information processing techniques and artefacts whose unifying concept is "the mathematical table".

An extensive summary of mathematical functions that occur in physical and engineering problems