HomeGroupsTalkZeitgeist
This site uses cookies to deliver our services, improve performance, for analytics, and (if not signed in) for advertising. By using LibraryThing you acknowledge that you have read and understand our Terms of Service and Privacy Policy. Your use of the site and services is subject to these policies and terms.
Hide this

Results from Google Books

Click on a thumbnail to go to Google Books.

e: The Story of a Number (Princeton…
Loading...

"e": The Story of a Number (Princeton Science Library) (original 1994; edition 2009)

by Eli Maor

MembersReviewsPopularityAverage ratingMentions
768818,218 (3.66)2
Member:tungsten_peerts
Title:"e": The Story of a Number (Princeton Science Library)
Authors:Eli Maor
Info:Princeton University Press (2009), Paperback, 248 pages
Collections:Read but unowned
Rating:
Tags:None

Work details

e: The Story of a Number by Eli Maor (1994)

None.

Loading...

Sign up for LibraryThing to find out whether you'll like this book.

No current Talk conversations about this book.

» See also 2 mentions

English (7)  German (1)  All languages (8)
Showing 1-5 of 7 (next | show all)
This book has been very satisfying for me to read so far since I have enough background to understand the math fairly easily, but at the same time the topics are unfamiliar to me.

Detailed Review:

Preface: The author explains his interest in e, identifies himself as a person born long enough ago that he had to make practical use of log tables, and as someone born in Israel.

1. John Napier, 1614
Napier's log tables take over the world! This was a lot history and the math didn't make sense to me. I didn't dig in very deeply, because Napier's logs are now obsolete. They were a revolution, though. There is a basic explanation of the general idea of doing multiplication with logarithms. Then follows a discussion of the fact that in Napier's day fractional exponents were unknown and unused and so his choice of base was dictated by this problem: that the powers must change rather slowly wrt. to their integer exponents so that the number must be close to 1 and also the extreme difficulty of manual computation. This makes me think of Babbage, eager to solve the problem of the construction of log tables. Euler's definitions of logarithms, which is not the same as Napier's, is now the canonical one.

2. Recognition
Logarithms are loved and the slide rule and its many cousins are invented, used, and made obsolete by the hand held calculator.

* Computing with Logarithms
A worked example of computation using log tables.

3. Financial Matters
e = the value you would get in a year if you invested a dollar at 100% interested compounded continually = (1 + 1/n)^n.

4. To the Limit: If it Exists
We have problems figuring out the limit, and must do close analysis, if two values tend in the opposite direction. These are the so called "indeterminate forms". We can expand (1 + 1/n)^n using the binomial theorem (Maor does not derive the binomial theorem). It is expanded to 1 + n * 1/n + n (n - 1)/2! * (1/n)^2 + n(n - 1)(n-2)/3! * (1/n)^3 + ... + (1/n)^n. This can be simplified to 1 + n * 1/n + (1 - 1/n)/2! + (1 - 1/n)(1-2/n)/3! + ... + 1/n^n. We want the limit as n approaches inf. That's 1/0! + 1/1! + 1/2! + .... Note how we ignore the last term in the previous expression because n is going to infinity and so there is no last term. This is a good way to compute e because it converges very fast.

* Some Curious Numbers Related to e
A grab bag. Maybe I'll go back to them later.

5. Forefathers of the Calculus
Squaring the circle in Egypt. A circle of diameter d has the same area as a square of side 8/9d. Run the numbers and pi is 256/81, which isn't too bad an approximation. Archimedes pursues the method of exhaustion. The Greeks were a little hindered by their strong inclination toward geometry rather than algebra. They had no x, and they specified line segments via their endpoints. The Greeks did not like the concept of infinity and Archimedes avoided it. The method of exhaustion had an ad-hoc quality to it, it required ingenuity.

6. Prelude to Breakthrough
In the 1500s Francois Viete wrote down an infinite product. Others followed suit and in the 1600 James Gregory wrote down an interesting infinite series. Kepler works with indivisibles, sometimes for practical purposes as in his "New Solid Geometry of Wine Barrels".

* Indivisibles at Work
A discussion of finding the area under the graph of the function f(x) = x^2 from 0 to a by means of the method of indivisibles. Chop the x axis into equal lengths of infinite smallness, d. Intervals are d, 2d, 3d, etc. f(d) = d^2, f(2d) = (2d)^2, etc. Therefore, area is d[d^2 + (2d)^2 + ... + (nd)^2]. But this can be simplified by taking out d, so we get d^3[1 + 2^2 + ... _ n^2]. But there's a formula for the sum of a sequence of squares, so this is: (1 + 1/n)(2 + 1/n)(nd)^3/6. But nd = a, so (1 + 1/n)(2 + 1/n)a^3/6. Now there is no indeterminacy, so as n goes to infinity we get 1*2*a^3/6 = a^3/6. This is obviously correct by the calculus, but we need to know how to find the sum of this series of squares, so it wasn't exactly automatic.
1 vote themulhern | Nov 17, 2018 |
Reading this book had me wondering about the mystical properties of numbers, whether there was some elemental truth I could discover. Overall, the book was an enjoyable and illuminating examination of e, and a solid retelling of e's importance in the development of trigonometry. ( )
1 vote James.Igoe | Jul 26, 2017 |
I doubt this book appeals to readers with 'modest background in mathematics' as the cover promises. 'e' is the base of the natural logarithm. I vaguely recalled that e was the only number that was its own derivative. This book is at its best describing the discovery of 'e', and its historical import.

As a non-mathematician I had to skip the most complicated moments, but still appreciated the overall story. ( )
  kcshankd | Jan 18, 2016 |
Mathematics, History ( )
  daudzoss | Jul 29, 2012 |
Like its more famous cousin pi, e is an irrational number that shows up in unexpected places all over mathematics. It also has a much more recent history, not appearing on the scene until the 16th century. My favorite parts of this book were the historical anecdotes such as the competitive Bernoullis and the Nerwton-Leibniz cross-Channel calculus feud. Unfortunately, this math history text is much heavier on the math than the history, including detailed descriptions of limits, derivatives, integrals, and imaginary numbers. The trouble with this large number of equationsis that if you’re already familiar with the concepts you’ll be doing a lot of skimming, but if the subject is confusing then reading this book will probably not give you any new insights. In short, as much as I normally enjoy books about math and science, this particular one felt too much like a textbook. Recommended only for those folks with a very strong love for the calculus and related topics. ( )
  melydia | Feb 28, 2012 |
Showing 1-5 of 7 (next | show all)
no reviews | add a review
You must log in to edit Common Knowledge data.
For more help see the Common Knowledge help page.
Series (with order)
Canonical title
Original title
Alternative titles
Original publication date
People/Characters
Important places
Important events
Related movies
Awards and honors
Epigraph
Dedication
In memory of my parents, Richard and Luise Metzger
First words
Rarely in the history of science has an abstract mathematical idea been received more enthusiastically by the entire scientific community than the invention of logarithms.
Quotations
Last words
Disambiguation notice
Publisher's editors
Blurbers
Publisher series
Original language
Canonical DDC/MDS
Book description
Haiku summary

Amazon.com Amazon.com Review (ISBN 0691058547, Paperback)

Until about 1975, logarithms were every scientist's best friend. They were the basis of the slide rule that was the totemic wand of the trade, listed in huge books consulted in every library. Then hand-held calculators arrived, and within a few years slide rules were museum pieces.

But e remains, the center of the natural logarithmic function and of calculus. Eli Maor's book is the only more or less popular account of the history of this universal constant. Maor gives human faces to fundamental mathematics, as in his fantasia of a meeting between Johann Bernoulli and J.S. Bach. e: The Story of a Number would be an excellent choice for a high school or college student of trigonometry or calculus. --Mary Ellen Curtin

(retrieved from Amazon Thu, 12 Mar 2015 18:06:47 -0400)

(see all 2 descriptions)

Interest earned on a bank account . . . arrangement of seeds in a sunflower . . . the shape of the Gateway Arch in St. Louis . . . are all intimately connected with the mysterious number "e". In this informal and engaging history, Eli Maor portrays the curious characters and the mathematics that lie behind the number e. Designed for a reader with only a modes background in mathematics, this book brings out e's central importance in mathematics. Illustrated.… (more)

(summary from another edition)

» see all 2 descriptions

Quick Links

Popular covers

Rating

Average: (3.66)
0.5
1
1.5
2 5
2.5 4
3 17
3.5 6
4 34
4.5 5
5 7

Is this you?

Become a LibraryThing Author.

 

About | Contact | Privacy/Terms | Help/FAQs | Blog | Store | APIs | TinyCat | Legacy Libraries | Early Reviewers | Common Knowledge | 135,731,974 books! | Top bar: Always visible