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Enlightening SymbolsA Short History of Mathematical Notation and Its Hidden Powers$
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Joseph Mazur

Print publication date: 2016

Print ISBN-13: 9780691173375

Published to Princeton Scholarship Online: January 2018

DOI: 10.23943/princeton/9780691173375.001.0001

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The Good Symbol

The Good Symbol

Chapter:
(p.189) Chapter 21 The Good Symbol
Source:
Enlightening Symbols
Author(s):

Joseph Mazur

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691173375.003.0021

This chapter argues that a good symbol should tell a whole story, must have an intelligence of its own, and must be a guide to our own intelligence. It begins with a discussion of the symbol π‎, which first appeared in 1706 and was used by William Jones to denote the ratio of the circumference to the diameter of a circle. The chapter suggests that π‎ evokes notions that might not surface with symbols carrying too much baggage. It then considers how mathematics abstractions and generalizations are applied to something relevant to Earth's existence and how mathematicians use imaginary exponents. It also describes the emergence of a new notion: that magnitude, direction, rotation may be embodied in the symbol itself. Finally, it explains what good mathematical notation is and asserts that whatever a symbol is, it must function as a revealer of patterns, a pointer to generalizations.

Keywords:   symbols, π‎, William Jones, notation, mathematics, exponents

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