By Irving Adler

ISBN-10: 0486498514

ISBN-13: 9780486498515

More than a hundred routines with solutions and two hundred diagrams remove darkness from the textual content. lecturers, scholars (particularly these majoring in arithmetic education), and mathematically minded readers will savor this amazing exploration of the position of geometry within the improvement of Western clinical thought.

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**Extra resources for A New Look at Geometry**

**Sample text**

If m is any counting number, and n is any counting number except 0, we use the labels and respectively for the points to the right and left of 0 at a distance of units. The points labeled in this way constitute the rational number system. Each rational number is represented by many equivalent fractions. Rational numbers may be added and multiplied in accordance with the familiar rules Fields The operations addition and multiplication in the rational number system have the following properties: If x, y and z are any rational numbers, 1.

We shall encounter it again on page 57 when we discuss some mathematical ideas related to the concept of motion. Mathematical Space The physical space occupied by a physical object is part of the physical world. Consequently, geometry as the study of physical space is really a branch of the science of physics. Geometry became a branch of mathematics only when it was transformed into the study of mathematical space, a conceptual structure obtained through the idealization of physical space. C. ).

For example, the rational number system is part of the field of real numbers, and the rational number system is itself a field. It is shown in the theory of fields that among all the fields that lie within a given field there is a smallest field that is contained in every one of them. Moreover, this smallest field is either the rational number system or one of the fields Fp. These smallest possible fields are called prime fields. The prime field contained in a finite field cannot be the rational number system, since the rational number system contains infinitely many members.

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