Softcover ISBN:  9781470447991 
Product Code:  SPEC/96 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781470448356 
Product Code:  SPEC/96.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Softcover ISBN:  9781470447991 
eBook: ISBN:  9781470448356 
Product Code:  SPEC/96.B 
List Price:  $120.00 $92.50 
MAA Member Price:  $90.00 $69.38 
AMS Member Price:  $90.00 $69.38 
Softcover ISBN:  9781470447991 
Product Code:  SPEC/96 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781470448356 
Product Code:  SPEC/96.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Softcover ISBN:  9781470447991 
eBook ISBN:  9781470448356 
Product Code:  SPEC/96.B 
List Price:  $120.00 $92.50 
MAA Member Price:  $90.00 $69.38 
AMS Member Price:  $90.00 $69.38 

Book DetailsSpectrumVolume: 96; 2018; 176 pp
Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (\( \varphi, \Pi, e\), and \(i\)), each of which has recently been the individual subject of historical and mathematical expositions. But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus.
This material offers an excellent excuse to display the power of calculus to reveal elegant truths that are not often seen in college classes. These truths are described here via the work of such luminaries as Nilakantha, Liu Hui, Hemachandra, Khayyam, Newton, Wallis, and Euler.

Table of Contents

Chapters

1. $\varphi $

2. $\pi $

3. $e$

4. $i$

A. Wallis’s original derivation of his formula for $\pi $

B. Newton’s original generalized binomial theorem


Reviews

This book can be used as a refresher on these aspects of the history of mathematics, and it could also work well for someone who is interested in the inner working of past mathematical geniuses' minds and the coincidences that make math so beautiful.
Kevin W. Pledger, Mathematics Teacher


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Reviews
 Requests
Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (\( \varphi, \Pi, e\), and \(i\)), each of which has recently been the individual subject of historical and mathematical expositions. But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus.
This material offers an excellent excuse to display the power of calculus to reveal elegant truths that are not often seen in college classes. These truths are described here via the work of such luminaries as Nilakantha, Liu Hui, Hemachandra, Khayyam, Newton, Wallis, and Euler.

Chapters

1. $\varphi $

2. $\pi $

3. $e$

4. $i$

A. Wallis’s original derivation of his formula for $\pi $

B. Newton’s original generalized binomial theorem

This book can be used as a refresher on these aspects of the history of mathematics, and it could also work well for someone who is interested in the inner working of past mathematical geniuses' minds and the coincidences that make math so beautiful.
Kevin W. Pledger, Mathematics Teacher