Central angle intersection points and of the legs of the angle with the circle form a diameter, then is a straight angle. (In radians, .) Let be the minor arc of the circle between points and , and let be the radius of the circle. If the central angle is subtended by , then If the central angle is not subtended by the minor arc , then is a reflex angle and If a tangent at and a tangent at intersect at the exterior point , then denoting the center as , the angles (convex) and are supplementary (sum to 180°). A
Revolutions in Mathematics Revolutions in Mathematics Revolutions in Mathematics is a collection of essays in the history and philosophy of mathematics. The book was reviewed by Pierre Kerszberg for "Mathematical Reviews" and by Michael S. Mahoney for "American Mathematical Monthly". Mahoney says "The title should have a question mark." He sets the context by referring to paradigm shifts that characterize scientific revolutions as described by Thomas Kuhn in his book "The Structure of Scientific Revolutions". According to Michael Crowe in chapter one, revolutions never occur in mathematics. Mahoney explains how mathematics grows upon itself and does not discard earlier gains in understanding with