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Pythagoras' LegacyMathematics in Ten Great Ideas$
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Marcel Danesi

Print publication date: 2020

Print ISBN-13: 9780198852247

Published to Oxford Scholarship Online: January 2020

DOI: 10.1093/oso/9780198852247.001.0001

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A very special number

(p.82) 6 e
Pythagoras' Legacy

Marcel Danesi

Oxford University Press

The number e, which is equal to 2.71828…, might seem like something trivial—a play on numbers by mathematicians. Nothing could be further from the truth. It is defined as the limit of the expression (1 + 1/n)n as n becomes large without bound. What possible connection does this number have with other areas of mathematics? As it turns out, it forms the base of natural logarithms; it appears in equations describing growth and change; it surfaces in formulas for curves; it crops up frequently in probability theory; and it appears in formulas for calculating compound interest. It is another example of how the ideas in mathematics are not isolated ones, but highly interrelated. The purpose of this chapter is, in fact, to link e to other great ideas, showing how mathematical discovery forms a chain—a chain constructed with a handful of fundamental ideas that appear across time and space, finding form and explanation in the writings and musings of individual mathematicians.

Keywords:   Euler’s number, exponential equations, Euler’s identity

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