The History of Mathematics: A Brief Course

This first part of our history is concerned with the "front end" of mathematics (to use an image from computer algebra)—its rela ...

Chapter 1. The Origin and Prehistory of Mathematics In this chapter we have two purposes: first, to consider what mathematics is ...

4 1. THE ORIGIN AND PREHISTORY OF MATHEMATICS considered as the study of processes inverse to those of arithmetic, was originall ...

NUMBERS 5 alphabetical ordering. These two notions are not so independent as they may appear in this illustration, however. Ex ...

6 1. THE ORIGIN AND PREHISTORY OF MATHEMATICS One can thus observe in children the capacity to recognize groups of two or three ...

CONTINUOUS MAGNITUDES 7 The Veronice wolf bone, from the Illustrated London News, Octo- ber 2, 1937. two vessels of different ...

8 1. THE ORIGIN AND PREHISTORY OF MATHEMATICS Frisch (1886-1982), and his work has been continued by James L. Gould and Carol Gr ...

SYMBOLS 9 relationships of geometry—distinguishing a square from an ellipse, for example were not mastered until later. 2.3. G ...

THE ORIGIN AND PREHISTORY OF MATHEMATICS FIGURE 1. A graph for which a unicursal tracing is possible. Once numbers have been r ...

SYMBOLS 11 the end, the left hand contains either five or nine sticks. After a sequence of such procedures, a final step begin ...

12 1. THE ORIGIN AND PREHISTORY OF MATHEMATICS type, "If 3 bananas cost 75 cents, how much do 7 bananas cost?" occur in the work ...

MATHEMATICAL INFERENCE 13 FIGURE 2. (a) The diagonal AC divides the rectangle ABCD into congruent triangles ABC and CD A. (b) ...

14 1. THE ORIGIN AND PREHISTORY OF MATHEMATICS head; another tossed its head back; yet another made pecking motions toward the f ...

QUESTIONS AND PROBLEMS 15 choosing a quantity of flour whose ratio to the standard cup is 1:3. Suppose that you have a standard ...

16 1. THE ORIGIN AND PREHISTORY OF MATHEMATICS 1.16. Logic enters the mathematics curriculum in high-school geometry. The rea- s ...

QUESTIONS AND PROBLEMS 17 FIGURE 3. (a) Line DE divides triangle ABC into triangle DEB and trapezoid ACED. (b) Line FGIH bisects ...

18 1. THE ORIGIN AND PREHISTORY OF MATHEMATICS are equally likely. Hence the probability of this new event F is 1/2. Thus, even ...

Chapter 2. Mathematical Cultures I In Chapter 1 we looked at the origin of mathematics in the everyday lives of people. The evid ...

20 2. MATHEMATICAL CULTURES I arithmetic and geometry, they come to astronomy, and Socrates (the narrator of the dialogue) repor ...

INDIA 21 As Plato said, one class of people will find this argument a sufficient justification for being a mathematician; anot ...