Doctrine of Triangles (eBook)

A History of Modern Trigonometry

Glen Van Brummelen (Autor)

eBook Download: PDF

2021
392 Seiten
Princeton University Press (Verlag)
978-0-691-21987-5 (ISBN)

Infos

An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentiethThe Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology.Following its uses in mid-sixteenth-century Europe as the foot of the ladder to the stars and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry's participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms.A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry's rich historical past full circle into the modern era.

Produkt-Details

• Erscheint lt. Verlag: 8.6.2021
• Zusatzinfo: 122 b/w illus. 6 tables.
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber ► Natur / Technik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Schlagworte: A0 • abraham de moivre • abstract algebra • Alexis Clairaut • Algebraic solution • Analogy • Angle trisection • Anton von Braunmühl • Arithmetica • Arithmetica universalis • Astronomy • Barycentric coordinate system • bisection • Blaise Pascal • Board of Longitude • Bureau des longitudes • Calculation • Calendrical calculation • Charles Babbage • Chinese mathematicians • Chinese trigonometry • Christopher Clavius • circumference • coefficient • Computation • coordinate system • CORDIC • Daniel Bernoulli • diagram • Diagram (category theory) • difference engine • differential equation • Differential Equations • Differentiation of trigonometric functions • Division algorithm • Eli Maor • Elliptic Integral • Equation • Erasmus Reinhold • Euclidean Geometry • Euler • Euler Method • Fourier series • Geodesy • geometric progression • Geometry • gradians • Haversine formula • haversines • Henry Briggs (mathematician) • Hipparchus • History of Mathematics • History of Science • Horner's method • Hyperbolic function • Hyperbolic Geometry • hyperbolic trigonometry • Hypotenuse • I0 • Infinitesimal • Integral of the secant function • Integration by parts • Inverse function • inverse trigonometric functions • Isaac Barrow • Jacob Bernoulli • Jesuit mathematicians • Jesuits • John Machin • Kepler's equation • law of tangents • Line segment • logarithm • Mathematical Analysis • mathematical education • Mathematical instrument • mathematician • math pedagogy • Maxima and minima • Menelaus' theorem • Metric system • Mollweide's formula • Newton's method • Notation • On the Sphere and Cylinder • oscillatory phenomena • parallelogram • Pascal's theorem • Pascal's triangle • plane astronomy • Principia Mathematica • Prosthaphaeresis • Pythagorean Theorem • quadratic function • Quantity • Radian • radians • Rational trigonometry • regiomontanus • Rheticus • Right triangle • Robert Waddington (mathematician) • Roger Cotes • Semiperimeter • Series (mathematics) • Simon Stevin • sine • Sine quadrant • Solution of triangles • spherical astronomy • Spherical law of cosines • Spherical trigonometry • square root • Srinivasa Ramanujan • Summation • Surveying • Textbook • The Doctrine of Chances • Theorem • Thomas Fincke • Thomas Harriot • Trigonometric Delights • Trigonometric Functions • Trigonometric Series • Trigonometry • Unit circle • Unit sphere • Variable (mathematics) • versines
• ISBN-10: 0-691-21987-7 / 0691219877
• ISBN-13: 978-0-691-21987-5 / 9780691219875