Numbers and geometry
Numbers and Geometry is a beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis, and geometry - meet. The aim of this book is to give a broad view of these subjects at the level of calculus, without being a calculus (or a pre-calculus) book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of m…
Read More ↓Title Statements
- Full title :Numbers and geometry / John Stillwell.
Summary
Numbers and Geometry is a beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis, and geometry - meet. The aim of this book is to give a broad view of these subjects at the level of calculus, without being a calculus (or a pre-calculus) book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. The key is algebra, which brings arithmetic and geometry together, and allows them to flourish and branch out in new directions.
Read More ↓Edition Statements
- Publication Date:©1998.
Publication Statements
- Publisher(s):Springer
- Place of Publication:New York
- Language:eng
- Publication Date:©1998.
The Physical Object
- Description:xiv, 339 pages : : illustrations ; : 24 cm.
Edition Identifiers
- ISBN:0387982892, 9780387982892, 9781461268673, 1461268672
- oclc:ocm37004483
- LC Classification:QA39.2
- Dewey Decimal:510
Table of Contents
Arithmetic : The natural numbers ; Division, divisors, and primes ; The mysterious sequence of primes ; Integers and rationals ; Linear equations ; Unique prime factorization ; Prime factorization and divisors ; Induction ; Foundations -- Geometry : Geometric intuition ; Constructions ; Parallels and angles ; Angles and circles ; Length and area ; The Pythagorean theorem ; Volume ; The whole and the part -- Coordinates : Lines and circles ; Intersections ; The real numbers ; The line ; The Euclidean plane ; Isometries of the Euclidean plane ; The triangle inequality ; Klein’s definition of geometry ; The non-Euclidean plane -- Rational points : Pythagorean triples ; Pythagorean triples in Euclid ; Pythagorean triples in Diophantus ; Rational triangles ; Rational points on quadratic curves ; Rational points on the sphere ; The area of rational right triangles -- Trigonometry : Angle measure ; Circular function ; Addition formulas ; A rational addition formula ; Hilbert’s third problem ; The dehn variant ; Additive functions ; The tetrahedron and the cube -- Finite arithmetic : Three examples ; Arithmetic mod n ; The ring ℤ/nℤ ; Inverses mod n ; The theorems of Fermat and Wilson ; T…
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