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The Doctrine of Triangles

A History of Modern Trigonometry

Glen Van Brummelen

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth

The 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.

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Schlagwörter

Division algorithm, Law of tangents, Logarithm, Maxima and minima, Quadratic function, Isaac Barrow, Bureau des Longitudes, Mathematical instrument, Spherical law of cosines, Prosthaphaeresis, Arithmetica, Diagram, Mathematician, Variable (mathematics), Square root, Coefficient, I0, Textbook, Hypotenuse, Roger Cotes, Pythagorean theorem, Calendrical calculation, Summation, Unit circle, Haversine formula, Parallelogram, Trigonometric functions, Euclidean geometry, Integral of the secant function, Charles Babbage, Differential equation, Metric system, Barycentric coordinate system, Pascal's triangle, Series (mathematics), Sine quadrant, Inverse function, Analogy, Integration by parts, Elliptic integral, Geometry, Abraham de Moivre, Astronomy, Semiperimeter, A0, Algebraic solution, Menelaus' theorem, Mollweide's formula, Newton's method, Bisection, Right triangle, Blaise Pascal, Geometric progression, John Machin, Solution of triangles, Coordinate system, Differentiation of trigonometric functions, Rational trigonometry, The Doctrine of Chances, Kepler's equation, Simon Stevin, Regiomontanus, Arithmetica Universalis, Geodesy, Abstract algebra, Hyperbolic geometry, Trigonometry, Unit sphere, Diagram (category theory), Henry Briggs (mathematician), Radian, Sine, Computation, Notation, Spherical trigonometry, Equation, Inverse trigonometric functions, Euler method, Trigonometric series, Infinitesimal, Thomas Harriot, Line segment, Daniel Bernoulli, Principia Mathematica, Angle trisection, Jacob Bernoulli, Theorem, Alexis Clairaut, Difference engine, Circumference, Hyperbolic function, Pascal's theorem, Robert Waddington (mathematician), Surveying, Horner's method, On the Sphere and Cylinder, Board of Longitude, Calculation, Quantity, Christopher Clavius