Leseprobe
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The Doctrine of Triangles
Glen Van Brummelen
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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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Pythagorean theorem, The Doctrine of Chances, Horner's method, Integral of the secant function, I0, Integration by parts, Thomas Harriot, Analogy, Differentiation of trigonometric functions, Arithmetica Universalis, Trigonometric series, Summation, Astronomy, Elliptic integral, Menelaus' theorem, Metric system, Arithmetica, Abraham de Moivre, Mollweide's formula, Equation, Abstract algebra, Calendrical calculation, Barycentric coordinate system, John Machin, Circumference, Euclidean geometry, Geometry, Euler method, Charles Babbage, Daniel Bernoulli, Unit sphere, Inverse function, Regiomontanus, On the Sphere and Cylinder, Hyperbolic geometry, Diagram (category theory), Notation, Roger Cotes, Coordinate system, Difference engine, Newton's method, Spherical trigonometry, Trigonometry, Hyperbolic function, Unit circle, Pascal's theorem, Surveying, Inverse trigonometric functions, Maxima and minima, Kepler's equation, Theorem, Alexis Clairaut, Logarithm, Mathematician, Solution of triangles, Angle trisection, Right triangle, Calculation, Hypotenuse, Trigonometric functions, Henry Briggs (mathematician), Haversine formula, Sine quadrant, Variable (mathematics), Pascal's triangle, Prosthaphaeresis, Spherical law of cosines, Quantity, Rational trigonometry, Geometric progression