Divine Proportions: Rational Trigonometry to Universal Geometry

N J Wildberger, "Divine Proportions: Rational Trigonometry to Universal Geometry"


2005 | ISBN-10: 097574920X | 320 pages | PDF | 3 MB

This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell"s law. Examples over finite fields are also included.

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Caught in the Crossfire: Revolution, Repression and the Rational Peasant

Caught in the Crossfire: Revolution, Repression and the Rational Peasant by T. David Mason


English | 28 Jan. 2004 | ISBN: 0742525384 | 328 Pages | PDF | 6 MB

Caught in the Crossfire presents a multifaceted explanation of why people participate in something as dangerous and uncertain as a revolutionary movement. Beginning with an analysis of the grievances that motivate peasant participation in political movements, the book also explores the additional factors_leadership, resources, and strategies_required to mobilize peasants for collective action. Collective action itself need not be violent, but a repressive state response can quickly transform a reformist movement into a revolution. Mason shows how different strategies on the part of various actors can result in a government victory, a rebel victory, or a negotiated settlement. The book concludes with a look to the future: Will the emerging trends toward political democratization and economic globalization make revolution in the countryside more or less likely?

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