The history of mathematics

Includes bibliographical references (pages 180-182)This paper is designed to provide a source of material for use in a one semester's course in the history of mathematics at the high school level. It has been written for use either as a supplement for a textbook or as an independent source in the absence of a textbook. It also provides material to enrich any other mathematics course. Emphasis has been placed on mathematical content and aspects of the history. While there is sufficient descriptive material, a considerable amount of material is included designed for the mathematically mature student. For example, there is a rather complete discussion in Chapter I of the three famous construction problems including their historical importance, solutions, and a proof of their inconstructibility using traditional Euclidean tools--compass and unmarked straight edge. The work has been divided into three chapters--the history of geometry, the development of arithmetic and algebra, and the development of logic and set theory. Chapter I traces the development of geometry from its beginnings in antiquity through Euclidean fruition during the magnificent period of ancient Greece. The remainder of the chapter examines the nature of each of the more important varieties including non-Euclidean geometry, projective and analytic geometry, topology, and the Erlangen Programme of Felix Klein. Chapter II examines the history of numeration, the Eudoxian solution to the problem of irrational magnitudes, major theorems from Greek number theory, Cardano's solution of the cubic equation, modern algebra and quaternions. Chapter III discusses the important properties of a postulational system, Cantor's theory of infinite sets, and Boole's universal language. There are also five appendices--A., The life and times of Pythagoras and the Pythagoreans; B., A proof of the fundamental theorem of algebra; C., A summary of Godel's proof of the incompleteness theorem; D., Euclid's proof of the Pythagorean theorem; and E., Babylonian texts