Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century This book brings to the non-specialist interested in mathematics many interesting results.
It can be recommended for seminars and will be enjoyed by the broad mathematical community. Ptolemy's Almagest is one of the most influential scientific works in history.
A masterpiece of technical exposition, it was the basic textbook of astronomy for more than a thousand years, and still is the main source for our knowledge of ancient astronomy.
This translation, based on the standard Greek text of Heiberg, makes the work accessible to English readers in an intelligible and reliable form. It contains numerous corrections derived from medieval Arabic translations and extensive footnotes that take account of the great progress in understanding the work made in this century, due to the discovery of Babylonian records and other researches.
It is designed to stand by itself as an interpretation of the original, but it will also be useful as an aid to reading the Greek text. The dramatic human story of an epic scientific quest and of one man's forty-year obsession to find a solution to the thorniest scientific dilemma of the day--"the longitude problem. Lacking the ability to measure their longitude, sailors throughout the great ages of exploration had been literally lost at sea as soon as they lost sight of land.
Thousands of lives and the increasing fortunes of nations hung on a resolution. One man, John Harrison, in complete opposition to the scientific community, dared to imagine a mechanical solution-a clock that would keep precise time at sea, something no clock had ever been able to do on land. Longitude is the dramatic human story of an epic scientific quest and of Harrison's forty-year obsession with building his perfect timekeeper, known today as the chronometer.
Full of heroism and chicanery, it is also a fascinating brief history of astronomy, navigation, and clockmaking, and opens a new window on our world.
Author : Peter A. Burrough,Christopher D. Lloyd,Rachel A. Author : F. Landis Markley,John L. This book explores topics that are central to the field of spacecraft attitude determination and control. The authors provide rigorous theoretical derivations of significant algorithms accompanied by a generous amount of qualitative discussions of the subject matter.
The book documents the development of the important concepts and methods in a manner accessible to practicing engineers, graduate-level engineering students and applied mathematicians.
Subject matter includes both theoretical derivations and practical implementation of spacecraft attitude determination and control systems.
It provides detailed derivations for attitude kinematics and dynamics and provides detailed description of the most widely used attitude parameterization, the quaternion. This title also provides a thorough treatise of attitude dynamics including Jacobian elliptical functions. It is the first known book to provide detailed derivations and explanations of state attitude determination and gives readers real-world examples from actual working spacecraft missions.
The subject matter is chosen to fill the void of existing textbooks and treatises, especially in state and dynamics attitude determination. Author : Christoph J. The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century.
Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe.
Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries.
Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era.
Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work.
Grattan-Guinness Middlesex University London "Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically!
The authors have successfully combined the history of geometry with the general development of culture and history. The graphic design is also excellent. Drawing on a number of detailed historical case studies and visual analyses of many moon images, this work proposes an innovative understanding of the development of lunar cartography, and offers new insights on theoretical debates surrounding the nature of maps in general.
Over the past five decades, Earth observation has developed into a comprehensive system that can conduct dynamic monitoring of the land, the oceans and the atmosphere at the local, regional and even global scale. Remember that, in spherical geometry, the side of a triangle is the arc of a great circle, so it is also an angle.
Turn the sphere so that A is at the "north pole", and let arc AB define the "prime meridian". Now create a new set of axes, keeping the y-axis fixed and moving the "pole" from A to B i. The first equation is the transposed cosine rule , which is sometimes useful but need not be memorised. The second equation gives the sine rule. The cosine rule will solve almost any triangle if it is applied often enough.
The sine rule is simpler to remember but not always applicable. Note that both formulae can suffer from ambiguity: E. So, when applying either formula, check to see if the answer is sensible. If in doubt, recalculate using the other formula, as a check.
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