A New Look at Geometry by Irving Adler

By Irving Adler

This richly exact review surveys the advance and evolution of geometrical rules and ideas from precedent days to the current. as well as the connection among actual and mathematical areas, it examines the interactions of geometry, algebra, and calculus. The textual content proves many major theorems and employs numerous vital thoughts. Chapters on non-Euclidean geometry and projective geometry shape short, self-contained treatments.
More than a hundred workouts with solutions and 2 hundred diagrams light up the textual content. academics, scholars (particularly these majoring in arithmetic education), and mathematically minded readers will delight in this amazing exploration of the position of geometry within the improvement of Western clinical thought.

Introduction to the Dover version via Peter Ruane.

Show description

Read Online or Download A New Look at Geometry PDF

Best geometry & topology books

Mathematics in Ancient and Medieval India

Heritage of arithmetic in historic and medieval India

Handbook of Geometric Analysis, Vol. 2 (Advanced Lectures in Mathematics No. 13)

Geometric research combines differential equations and differential geometry. a tremendous element is to resolve geometric difficulties via learning differential equations. along with a few identified linear differential operators resembling the Laplace operator, many differential equations bobbing up from differential geometry are nonlinear.

Vector Bundles and Complex Geometry

This quantity encompasses a choice of papers from the convention on Vector Bundles held at Miraflores de l. a. Sierra, Madrid, Spain on June 16-20, 2008, which commemorated S. Ramanan on his seventieth birthday. the most parts coated during this quantity are vector bundles, parabolic bundles, abelian types, Hilbert schemes, touch constructions, index thought, Hodge concept, and geometric invariant idea.

Extra resources for A New Look at Geometry

Sample text

If s = m/n, then m2/n2 = s2 = 2, and m2 = 2n2. That is, m2 must be an even number. This implies that m is an even number, because if m were odd, m2 would also be odd. Consequently there exists a whole number k such that m = 2k. Then m2 = 4k2. But m2 = 2n2. Equating these two expressions for m2, we see that 2n2 = 4k2, or n2 = 2k2. That is, n2 must be even, and therefore n must be even. Notice that while m and n are not both even, we have been compelled to say that they are both even. We were led into this absurdity as a result of assuming that the length s may be expressed as a ratio of whole numbers.

Includes bibliographical references and index. Geometry. I. Title. com Contents Introduction to the Dover Edition 1 One Book and Three Metaphors 2 Geometry Before Euclid 3 Euclid’s 4 Geometry Geometry via Numbers 5 Geometry via Arrows 6 Geometry via Reflections 7 Geometry in Newtonian Physics 8 Non-Euclidean Geometry 9 The Calculus and Geometry 10 Projective Geometry 11 Geometry in Relativity Physics 12 Geometry Generalized 13 Geometry and Algebra Bibliography Answers to Exercises Index Introduction to the Dover Edition When it was first published in the USA by The John Day Company in 1966, this was, to my knowledge, the first book to provide an accessibly broad description of classical and modern geometries.

Thus introducing more points of division on the line. 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.

Download PDF sample

Rated 4.85 of 5 – based on 39 votes

Categories: Geometry Topology