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Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe.
«An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others.»--New York Times Book Review
Introduction
A Note to the Reader
The Frame of the Book
Masters of the Symbols
Symbols of the Masters
The Black Blossoms of Geometry
Cartesian Coordinates
The Unbearable Smoothness of Motion
Yo
Thirteen Ways of Looking at a Line
The Doctor of Discovery
Real World Rising
Forever Familiar, Forever Unknown
Some Famous Functions
Speed of Sorts
Speed, Strange Speed
Paris Days
Prague Interlude
Memory of Motion
The Dimpled Shoulder
Wrong Way Rolle
The Mean Value Theorem
The Song of Igor
Area
Those Legos Vanish
The Integral Wishes to Compute an Area
The Integral Wishes to Become a Function
Between the Living and the Dead
A Farewell to Continuity
Epilogue