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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 Explosion

The Explosion

(p.150) Chapter 16 The Explosion
Enlightening Symbols

Joseph Mazur

Princeton University Press

This chapter focuses on the Cartesian coordinate system and how it provides a link between geometry and algebra. In Geometria, René Descartes introduced a new idea for notation, a rule: beginning letters of the alphabet were to be reserved for fixed known quantities and letters from p onward were to represent variables or unknowns that could take on a succession of values. To this day, this division of the alphabet at p remains the loose standard rule. The chapter also considers the Pythagorean theorem as a way of finding the distance between any two points in space; how the algebraic operations of addition, subtraction, multiplication, division, and extraction of a square root could actually be performed; and who came up with the idea of the vinculum.

Keywords:   algebra, Cartesian coordinate system, geometry, Geometria, René Descartes, notation, alphabet, Pythagorean theorem, operations, vinculum

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