Spherical Trigonometry A Comprehensive Approach
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Author | : Ira Fajardo |
Publisher | : |
Total Pages | : 148 |
Release | : 2019-11-27 |
Genre | : |
ISBN | : 9781711990866 |
This unique book Spherical Trigonometry is the first and only book with comprehensive and accurate illustration of diagrams of spherical triangles according to given and computed angles that is not found in any similar books in circulation. Part 1, 2, and 3 consist of Definitions.Computations on spherical triangle areas, right, polar, quadrantal, oblique, and spherical triangles. Use of Napier's Rules, Laws of Sines and Cosines, The Six Cases, Delambre's and Gauss' Formulas. Part 4 consists of its application to sea and air navigation, statute and nautical mile, geographical coordinates of cities, computation of distances between cities of countries, time difference between countries, bearing, heading, and course.
Author | : Glen Van Brummelen |
Publisher | : Princeton University Press |
Total Pages | : 208 |
Release | : 2017-04-04 |
Genre | : Mathematics |
ISBN | : 0691175993 |
"Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth."--Jacket.
Author | : Marshall A. Whittlesey |
Publisher | : CRC Press |
Total Pages | : 262 |
Release | : 2019-11-14 |
Genre | : Mathematics |
ISBN | : 1000627527 |
Spherical Geometry and Its Applications introduces spherical geometry and its practical applications in a mathematically rigorous form. The text can serve as a course in spherical geometry for mathematics majors. Readers from various academic backgrounds can comprehend various approaches to the subject. The book introduces an axiomatic system for spherical geometry and uses it to prove the main theorems of the subject. It also provides an alternate approach using quaternions. The author illustrates how a traditional axiomatic system for plane geometry can be modified to produce a different geometric world – but a geometric world that is no less real than the geometric world of the plane. Features: A well-rounded introduction to spherical geometry Provides several proofs of some theorems to appeal to larger audiences Presents principal applications: the study of the surface of the earth, the study of stars and planets in the sky, the study of three- and four-dimensional polyhedra, mappings of the sphere, and crystallography Many problems are based on propositions from the ancient text Sphaerica of Menelaus
Author | : Dan Pedoe |
Publisher | : Courier Corporation |
Total Pages | : 466 |
Release | : 2013-04-02 |
Genre | : Mathematics |
ISBN | : 0486131734 |
Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.
Author | : Titu Andreescu |
Publisher | : Springer Science & Business Media |
Total Pages | : 222 |
Release | : 2006-03-04 |
Genre | : Mathematics |
ISBN | : 0817644326 |
* Problem-solving tactics and practical test-taking techniques provide in-depth enrichment and preparation for various math competitions * Comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry * A cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training
Author | : Norman John Wildberger |
Publisher | : |
Total Pages | : 330 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : |
"... introduces a remarkable new approach to trigonometry and Euclidean geometry, with dramatic implications for mathematics teaching, industrial applications and the direction of mathematical research in geometry" -- p. vii.
Author | : Xin-She Yang |
Publisher | : Dunedin Academic Press |
Total Pages | : 0 |
Release | : 2009 |
Genre | : Earth sciences |
ISBN | : 9781906716004 |
Any quantitative work in earth sciences requires mathematical analysis. Many mathematical methods are essential to the modeling and analysis of the geological, geophysical, and environmental processes widely studied in earth sciences. This book provides an introduction to the fundamental mathematics that all earth scientists need. Assuming nor more than a standard secondary school level as its starting point, the book is self-contained and provides an essential toolkit of basic mathematics for earth scientists. The topics of earth sciences are vast and multidisciplinary, and consequently the mathematical tools required by its students are diverse and complex. Introductory Mathematics for Earth Scientists strikes a fine balance between coverage and detail. Topics have been selected to provide a concise but comprehensive introductory coverage of all the major and popular mathematical methods. The book offers a 'theorem-free' approach with an emphasis on practicality. With dozens of step-by-step worked examples, the book is especially suitable for non-mathematicians and geoscientists. The topics include binomial theorem, index notations, polynomials, sequences and series, trigonometry, spherical trigonometry, complex numbers, vectors and matrices, ordinary differential equations, partial differential equations, Fourier transforms, numerical methods, and geostatistics. Introductory Mathematics for Earth Scientists introduces a wide range of fundamental and widely-used, mathematical methods. This book is ideal for both undergraduate students and postgraduate students. Additionally, it is a helpful reference for more advanced scientists.
Author | : Caspar Wessel |
Publisher | : Kgl. Danske Videnskabernes Selskab |
Total Pages | : 164 |
Release | : 1999 |
Genre | : Geometry |
ISBN | : 9788778761583 |
Author | : Glen Van Brummelen |
Publisher | : Princeton University Press |
Total Pages | : 352 |
Release | : 2021-08-10 |
Genre | : Mathematics |
ISBN | : 1400833310 |
The Mathematics of the Heavens and the Earth is the first major history in English of the origins and early development of trigonometry. Glen Van Brummelen identifies the earliest known trigonometric precursors in ancient Egypt, Babylon, and Greece, and he examines the revolutionary discoveries of Hipparchus, the Greek astronomer believed to have been the first to make systematic use of trigonometry in the second century BC while studying the motions of the stars. The book traces trigonometry's development into a full-fledged mathematical discipline in India and Islam; explores its applications to such areas as geography and seafaring navigation in the European Middle Ages and Renaissance; and shows how trigonometry retained its ancient roots at the same time that it became an important part of the foundation of modern mathematics. The Mathematics of the Heavens and the Earth looks at the controversies as well, including disputes over whether Hipparchus was indeed the father of trigonometry, whether Indian trigonometry is original or derived from the Greeks, and the extent to which Western science is indebted to Islamic trigonometry and astronomy. The book also features extended excerpts of translations of original texts, and detailed yet accessible explanations of the mathematics in them. No other book on trigonometry offers the historical breadth, analytical depth, and coverage of non-Western mathematics that readers will find in The Mathematics of the Heavens and the Earth.
Author | : Antoine-René Mauduit |
Publisher | : |
Total Pages | : 252 |
Release | : 1768 |
Genre | : Spherical trigonometry |
ISBN | : |