Inscribed angle "V" and whose sides pass through points "A" and "B". Draw line "OA". Angle "BOA" is a central angle; call it "θ". Lines "OV" and "OA" are both radii of the circle, so they have equal lengths. Therefore, triangle "VOA" is isosceles, so angle "BVA" (the inscribed angle) and angle "VAO" are equal; let each of them be denoted as "ψ". Angles "BOA" and "AOV" are supplementary. They add up to 180°, since line "VB" passing through "O" is a straight line. Therefore, angle "AOV" measures 180° − "θ". It is known that the three angles of a triangle add
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