Randolph Eck:
The number e is interesting beast. In this book, the author shows us how this constant is found in a variety of phenomena, such as physics, biology, art, and music. This number was actually known about half a century before the invention of calculus. It was referred to in Edward Wright’s English translation of John Napier’s work on logarithms, published in 1618. It also seems to have appeared in connection of a formula for compound interest. However, work on the area under a hyperbola seems to have led independently to the same number. Its origin appears shrouded in mystery. In the eighteenth century, Leonhard Euler’s work gave it a central role in calculus.
We start with an introduction into logarithms, and then segue into what e equates to. We learn that the number e is equal to the limit of (1 + 1/n) ^n as n tends toward infinity. This converges to 2.71828 rounded off. The concept of the limit is interesting. A sequence of numbers can approach a limit as closely as one wishes, but here’s the kicker: it never actually reaches it. Taking a step back in time we learn of the work of Archimedes and his method of exhaustion, where he successfully...
United States on Jun 25, 2021
Michel Alves:
Eu resolvi comprar esse livro porque um dia me surgiu uma dúvida. Por que o número e é utilizado como base padrão na função exponencial?
Comecei o livro com o intuito de responder a essa pergunta, mas na realidade o livro me levou muito além. Logo no primeiro capítulo me proporcionou um novo olhar sobre a função logarítmica. Daí para frente seguiram-se surpresas até o final. Com certeza, terminei o livro como uma pessoa melhor do que no início. Está mais que recomendado.
Brazil on Aug 22, 2020
Manjunath P:
Beautiful book describing everything about the number 'e'. Lots of historical descriptions all along the book, which will make the readers to understand the way mathematics evoloved.
India on Jan 19, 2020
sam:
I was reluctant at first, thought what, it's the trend now, a book for every number?! but then i got hooked on it for weeks. it's insightful and original, i enjoyed every chapter of it.
France on Feb 04, 2014
Bookologist:
Having read this book, I can say that the historical treatment was very interesting, putting flesh and bones to the finished product we all learn something about in Science and Engineering programs in school. The math for the most part was very easy to follow.
In the appendices, the proof of the constant angle between the radius and tangent for the logarithmic spiral is solved using complex numbers and conformal mapping. This is elegant in its simplicity but may be far from intuitive for many. An alternative method is to use rectangular coordinates with y = exp(a.theta)sin(theta), and x = exp(a.theta)cos(theta), and then expressing the tangent at a point on the curve with the derivative (dy/dtheta)/(dx/dtheta) and calling it tan(phi). The radius has angle theta, so we have tan(theta). Then we use the well-known identity for tan(phi - theta). Its a bit more lengthy but its also more intuitive to my way of thinking.
I found also, that the rectangular coordinate approach to the spiral length being equal to the tangential line segment from the tangent point to the vertical axis is a good alternative to the proof given in the appendices. It takes a bit...
Canada on Feb 12, 2013
Reading Fan:
This was a good book for someone who likes math and is willing to work a little. You should have had (and enjoyed at some point) a little algebra, geometry, and calculus. Even if your math is rusty like mine, you will be able to follow this book well enough. I was surprised how much of it came back to me. (I wouldn't want to be tested on it though!)
The most fascinating thing to me was the brainpower that thought this stuff up! How they could have pumped so much out of the natural logarithm (e) was simply amazing to me, things such as the elegant infinite series of fractions and continued fractions, continued exponentials, sometimes with factorials. Perhaps the most amazing thing was the totally unintuitive formula e raised to the power of the product of i and pi = -1; imagine e, i, and pi contained in one short,neat, little formula! This book is also about the history of math, how calculus was invented, and how imaginary numbers found their place in math. Fortunately for me, Eli Maor goes slow enough and skips enough of the details and the proofs to make this book readable. He also gives neat short biographies of the main characters in the history of...
United States on Apr 21, 2008
Khalifa Alhazaa:
This writer had written three books, as far as I know, the one before you, "Trigonometric Delights" and "To Infinity and Beyond." If this does not convince you to read this book, then nothing will.
I read this after Dr Beckmann's "A History of Pi," and found it to be the right choice. (for a review of that book click on the blue "a_mathematician" above to see it in its proper place). As Pi is closely associated with the circle, then so is e associated to logarithms and differential equations. It is even called the natural base!
Maor does an excellent job in accounting the historical points about e. In the beginning of the book we see e associated with the logarithms and then we see its characterization as the limit of some sequence of numbers. Then we go into some summary of the origin of calculus to see that the exponential function with base e is its own derivative.
If you find all this difficult to grasp right now, do not worry, because it is explained in the book in simple language.
The book then goes into spirals, and then to hyperbolic trig functions which are defined in terms of the exponential functions base e, and the book is concluded with...
United States on May 01, 2003
| Eli Maor's Fascinating Tale of the History of a Number | Preschool Math Workbook: Number Tracing, Addition, and Subtraction Exercises for Little Learners | Euclid's Elements: Later Printing Edition - An Essential Text for the Study of Geometry | |
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| B2B Rating |
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98
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| Sale off | $2 OFF | $4 OFF | |
| Total Reviews | 11 reviews | 66 reviews | 22 reviews |
| Number Theory (Books) | Number Theory | Number Theory | Number Theory |
| Dimensions | 5.5 x 0.5 x 8.5 inches | 8.5 x 0.25 x 11 inches | 7.12 x 1.18 x 10.07 inches |
| History & Philosophy of Science (Books) | History & Philosophy of Science | ||
| Language | English | English | English |
| Item Weight | 9 ounces | 9.6 ounces | 2.06 pounds |
| ISBN-13 | 978-0691168487 | 978-1697668575 | 978-1888009194 |
| Publisher | Princeton University Press; Reprint edition | Independently published | Green Lion Press; Later Printing edition |
| Customer Reviews | 4.4 4.4 out of 5 stars 330 ratings var dpAcrHasRegisteredArcLinkClickAction; P.when.execute { if { dpAcrHasRegisteredArcLinkClickAction = true; A.declarative { if { ue.count || 0) + 1); } } ); } }); P.when.execute { A.declarative{ if { ue.count || 0) + 1); } }); }); | 4.8 4.8 out of 5 stars 2,680 ratings var dpAcrHasRegisteredArcLinkClickAction; P.when.execute { if { dpAcrHasRegisteredArcLinkClickAction = true; A.declarative { if { ue.count || 0) + 1); } } ); } }); P.when.execute { A.declarative{ if { ue.count || 0) + 1); } }); }); | 4.8 4.8 out of 5 stars 898 ratings var dpAcrHasRegisteredArcLinkClickAction; P.when.execute { if { dpAcrHasRegisteredArcLinkClickAction = true; A.declarative { if { ue.count || 0) + 1); } } ); } }); P.when.execute { A.declarative{ if { ue.count || 0) + 1); } }); }); |
| Best Sellers Rank | #30 in Number Theory #130 in Mathematics History #706 in History & Philosophy of Science | #1 in Number Theory #523 in Children's Books | #29 in Number Theory #87 in Geometry & Topology #122 in Mathematics History |
| ISBN-10 | 0691168482 | 1697668577 | 1888009195 |
| Paperback | 227 pages | 108 pages | 529 pages |
| Mathematics History | Mathematics History | Mathematics History |
The author explains intricate concepts of mathematics in easy to understand way, although some preliminary mathematical training is necessary. The author claims that even person with a little knowledge of mathematics can read the book, however, I think that a good knowledge of high school math allows you to enjoy the book more. Besides nice explanation of math, I really enjoyed historical notes and stories which accompany any discovery in science.
The book is also very well organized. Every chapter is supplied with additional texts related to main subject of the chapter – for example another historical notes, practical application of explained concepts or interesting formulas and relations. There is also list of additional sources for further study at the end of each chapter. For readers more interested or trained in the subjects, some proofs are included in the appendix.
To conclude, I would recommend the book to anybody interested in history of mathematics,...
Germany on Jun 12, 2022