A Smoother Pebble: Mathematical Explorations

Front Cover
Oxford University Press, Oct 30, 2003 - Mathematics - 280 pages
0 Reviews
This book takes a novel look at the topics of school mathematics--arithmetic, geometry, algebra, and calculus. In this stroll on the mathematical seashore we hope to find, quoting Newton, "...a smoother pebble or a prettier shell than ordinary..." This book assembles a collection of mathematical pebbles that are important as well as beautiful.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Quadratic Equations
130
Secrecy Jealousy Rivalry Pugnacity and Guile
135
Solving a cubic equation
138
Symmetry Without Fear
142
Symmetries of a Square
145
The Group Axioms
148
Isometrics of the Plane
150
Patterns for Plane Ornaments
151

Magnitudes Ratio and Proportion
22
Method 1 proportion according to Eudoxus
24
Method 2 Attributed to Theaetetus
26
The Music of the Ratios
33
Acoustics
35
The rotating circle
36
Waveforms and spectra
39
Psychoacoustics
44
Consonance versus dissonance
45
Intervals Scales and Tuning
49
Approximating m octaves with n fifths
51
Equaltempered tuning
54
Tubeland
61
Curvature of Smooth Curves
62
Curves embedded in two dimensions
63
Curves embedded in three dimensions
64
Curvature of Smooth Surfaces
65
Gaussian curvature Extrinsic definition
66
Tubeland A fantasy
68
Triangular excess
71
Euclidean Geometry
73
The parallels axiom
75
Models of nonEuclidean geometries
77
The Calculating Eye
82
Graphs
84
The need for graphs
85
Materials for graphs
86
Clever people invented graphs
89
Coordinate Geometry
93
Synthetic versus analytic
94
Synthetic and analytic proofs
95
Straight lines
99
Conic sections
101
Algebra Rules
111
Algebra Anxiety
112
Arithmetic by Other Means
115
Symbolic algebra
116
Algebra and Geometry
120
Aljabr
121
Square root algorithms
122
The Root of the Problem
128
Graphical Solutions
129
Wallpaper watching
158
The Magic Mirror
160
The Magic Writing
162
On the Shoulders of Giants
167
Integration Before Newton and Leibniz
168
Circular reasoning
170
Completing the estimate of pi
171
Differentiation Before Newton and Leibniz
172
Descartess discriminant method
173
Fermats difference quotient method
176
Galileos Lute
177
The inclined plane
179
SixMinute Calculus
184
Preliminaries
185
Functions
186
Limits
188
Continuity
189
The Damaged Dashboard
191
The broken speedometer
193
The derivative
194
The broken odometer
199
The definite integral
201
Roller Coasters
206
Time of descent
208
RollerCoaster Science
212
The Simplest Extremum Problems
213
The lifeguards calculation
215
A faster track
217
A roadbuilding project for three towns
219
Inequalities
220
The inequality of the arithmetic and geometric means
221
Cauchys inequality
223
The geometry of the cycloid
227
A differential equation
228
The restricted brachistochrone
230
The unrestricted brachistochrone
235
Glossary
243
Notes
249
References
257
Index
261
Copyright

Other editions - View all

Common terms and phrases

Popular passages

Page 1 - I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

Bibliographic information