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Fabulous Fibonacci Numbers
The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.
392 pages, Hardcover
First published June 21, 2007
40 people are currently reading
390 people want to read
About the author
Alfred S. Posamentier
94 books31 followersAlfred S. Posamentier (born October 18, 1942) is among the most prominent American educators in the country and is a lead commentator on American math and science education, regularly contributing to The New York Times and other news publications. He has created original math and science curricula, emphasized the need for increased math and science funding, promulgated criteria by which to select math and science educators, advocated the importance of involving parents in K-12 math and science education, and provided myriad curricular solutions for teaching critical thinking in math.
Dr. Posamentier was a member of the New York State Education Commissioner’s Blue Ribbon Panel on the Math-A Regents Exams. He served on the Commissioner’s Mathematics Standards Committee, which redefined the Standards for New York State. And he currently serves on the New York City schools’ Chancellor’s Math Advisory Panel.
Posamentier earned a Ph.D. in mathematics education from Fordham University (1973), a Master’s degree in mathematics education from the City College of the City University of New York (1966) and an A.B. degree in mathematics from Hunter College of the City University of New York.
Posamentier was born in Manhattan in New York City, the son of Austrian immigrants. He has one daughter (Lisa, born in 1970), and one son (David, born in 1978). He resides in River Vale, New Jersey and is the current Dean of the School of Education and professor of mathematics education at Mercy College, New York. He was formerly professor of mathematics education and dean of the School of Education at The City College of the City University of New York, where he spent the previous 40 years.
Dr. Posamentier was a member of the New York State Education Commissioner’s Blue Ribbon Panel on the Math-A Regents Exams. He served on the Commissioner’s Mathematics Standards Committee, which redefined the Standards for New York State. And he currently serves on the New York City schools’ Chancellor’s Math Advisory Panel.
Posamentier earned a Ph.D. in mathematics education from Fordham University (1973), a Master’s degree in mathematics education from the City College of the City University of New York (1966) and an A.B. degree in mathematics from Hunter College of the City University of New York.
Posamentier was born in Manhattan in New York City, the son of Austrian immigrants. He has one daughter (Lisa, born in 1970), and one son (David, born in 1978). He resides in River Vale, New Jersey and is the current Dean of the School of Education and professor of mathematics education at Mercy College, New York. He was formerly professor of mathematics education and dean of the School of Education at The City College of the City University of New York, where he spent the previous 40 years.
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Displaying 1 - 21 of 21 reviews
June 2, 2016
Every book rating is subjective. I have no doubt that somewhere out are people who would love this book. I thought it was okay, but found myself unable to read it in any detail. I skimmed or skipped over a fair bit of material simply because I couldn't get my brain engaged with it.
Here's the trouble: it's a math book. I'm pretty good with math and have been known to play with numbers and formulae from time to time just for the fun of it. But these days I don't seem to have the mental stamina for reading math. Reading math isn't like reading text, at least not for those of us who don't do it all the time. For most of us, it takes considerable concentration. It's real work.
The authors are clearly in love with their subject and really, really want readers to fall in love with it too, but they are mathematicians and present the subject like mathematicians rather than popularizers. Result? A lot of math. And that's okay for readers who are into it, but I'm afraid that most people just aren't going to want to go there. Even some of us who are technically capable of going there might decide to take a pass.
On a side note, its rather ironic that my wife put this book into my hands during a trip to the library well after my first novel, The Fibonacci Murders , had been released. By then it was too late to serve as research material. Oh, well . . .
Here's the trouble: it's a math book. I'm pretty good with math and have been known to play with numbers and formulae from time to time just for the fun of it. But these days I don't seem to have the mental stamina for reading math. Reading math isn't like reading text, at least not for those of us who don't do it all the time. For most of us, it takes considerable concentration. It's real work.
The authors are clearly in love with their subject and really, really want readers to fall in love with it too, but they are mathematicians and present the subject like mathematicians rather than popularizers. Result? A lot of math. And that's okay for readers who are into it, but I'm afraid that most people just aren't going to want to go there. Even some of us who are technically capable of going there might decide to take a pass.
On a side note, its rather ironic that my wife put this book into my hands during a trip to the library well after my first novel, The Fibonacci Murders , had been released. By then it was too late to serve as research material. Oh, well . . .
August 29, 2025
Świetna książka! 😍 Zachwyciłam się ciągiem Fibonacciego, a wcześniej tylko przelotnie o nim słyszałam. Polecam! ❤️
January 31, 2022
Fascinating book to learn about many of the unexpected places where the Fibonacci sequence appears. It seems though that the value of the sequence is about identifying the breadth of those unexpected places that already exist and less about how the sequence can be applied to build, solve or create across a myriad of industries. Nevertheless, exceptionally insightful and digestible for those of us that aren't mathematicians.
November 25, 2024
Kindle rendition is AWFUL!!
The Kindle version of this book is an unmitigated disaster!! If any effort was made to anticipate the readability and functionality in an electronic reading experience, it was wholly inadequate.
Fractions, superscripts and subscripts as used become UNREADABLE - even when displayed full-screen on a 13 iPad Pro. On a smaller screen, they would be unreadable at the outset. I have to think that some of the graphics used are unreadable (without a magnifying glass) even in printed form
As for the content - - - fascinating as the Fibonacci Numbers and Golden Ratio may be, the authors have gone WAY beyond the fascination that anyone other that a hard-core mathematician might have. The math used in much of the discussion is FAR beyond the skill levels of 90% of the population (even those who can read)!
And their observation of the Golden Ratio in art, architecture and nature (except where it was intentionally employed) stretches credibility beyond the breaking point.
I’m a “math/science” guy and a card-carrying geek who even taught high school math for a time and I’m still in love with learning - but I skipped wide swaths of this book and ultimately gave up when the authors got into imposing their perceptions on art.
The Kindle version of this book is an unmitigated disaster!! If any effort was made to anticipate the readability and functionality in an electronic reading experience, it was wholly inadequate.
Fractions, superscripts and subscripts as used become UNREADABLE - even when displayed full-screen on a 13 iPad Pro. On a smaller screen, they would be unreadable at the outset. I have to think that some of the graphics used are unreadable (without a magnifying glass) even in printed form
As for the content - - - fascinating as the Fibonacci Numbers and Golden Ratio may be, the authors have gone WAY beyond the fascination that anyone other that a hard-core mathematician might have. The math used in much of the discussion is FAR beyond the skill levels of 90% of the population (even those who can read)!
And their observation of the Golden Ratio in art, architecture and nature (except where it was intentionally employed) stretches credibility beyond the breaking point.
I’m a “math/science” guy and a card-carrying geek who even taught high school math for a time and I’m still in love with learning - but I skipped wide swaths of this book and ultimately gave up when the authors got into imposing their perceptions on art.
December 7, 2022
A thick Maths book that full of suprises, intrigues and delights.. just like the Hercules Poirot movies that draw the audience into a welcoming mysterious journey. It took long time for me to complete this book as I jotted down notes, googled infos (Indian figures and numeral, understanding the George Bizet notes and test the sound waves, Lucas and Pascal numbers) . It provides good story telling as an introductions, which I hope will ignite students turning Maths as a specialty (the crisis we face today at the uni..dangerously small group of young people are interested in it)
It was a great book full of informations on interrelationship of Fibonacci with nature, our well being, financial (if u are a remisier or a trader). What make it easier to read this book(if you are doing research and curiosity machine 😬) it has a clear language, tables, diagrams and MOST IMPORTANTLY the appendixes with proofs of statements on page 349 (appendix B) that is awesome and extremely useful to get back to the chapter we have read about. In a simple word to express my opinion on this book - Elegance!
It was a great book full of informations on interrelationship of Fibonacci with nature, our well being, financial (if u are a remisier or a trader). What make it easier to read this book(if you are doing research and curiosity machine 😬) it has a clear language, tables, diagrams and MOST IMPORTANTLY the appendixes with proofs of statements on page 349 (appendix B) that is awesome and extremely useful to get back to the chapter we have read about. In a simple word to express my opinion on this book - Elegance!
July 23, 2022
A wonderful book I enjoyed a lot, very well written, with lots of examples and demonstrations, in the appendixes. Very well written, anyone interesting in maths can read it, just with high school math, doesn't need more and a good run with reading.
Amazed at how the Fibonacci number is related to the golden ratio and golden polygons.
Very interesting the applications that the Fibonacci numbers have on made-man activities as well as on nature.
The author makes an excellent point when he expresses that "We must be careful not to draw conclusions where they don't necessarily warranty" when it is applying the Golden Ratio or the Fibonacci numbers to historic artworks. Just because some proportions are approximate to the Golden Ratio or the Fibonacci numbers, doesn't mean they were intended to use, could be just our current era thinking that they were to use it.
Very nice analysis of music from a mathematical point of view and how often math design music failed to entice an audience.
Amazed at how the Fibonacci number is related to the golden ratio and golden polygons.
Very interesting the applications that the Fibonacci numbers have on made-man activities as well as on nature.
The author makes an excellent point when he expresses that "We must be careful not to draw conclusions where they don't necessarily warranty" when it is applying the Golden Ratio or the Fibonacci numbers to historic artworks. Just because some proportions are approximate to the Golden Ratio or the Fibonacci numbers, doesn't mean they were intended to use, could be just our current era thinking that they were to use it.
Very nice analysis of music from a mathematical point of view and how often math design music failed to entice an audience.
August 21, 2019
El llibre fa un repàs extens dels nombres de Fibonacci: des de les propietats més senzilles, a propietats més amagades, passant per diferents llocs (molts d'ells inesperats) on s'acaben trobant. Crec que és difícil que hi hagi alguna propietat dels nombres que no es trobi en el llibre.
Al principi ho demostra tot, després hi ha algun resultat que no demostra (i que no li hagués costat gaire, per no deixar amb les ganes al personal). Però és rigorós i bastant complet.
Com sempre passa amb els nombres de Fibonacci (o més aviat amb el nombre auri), hi ha moments en què sembla que el vulguin fer entrar amb calçador a tot arreu i que hagi de sortir-hi per força, però a banda d'això, la resta m'ha semblat molt bona.
Ara acabo de veure que els mateixos autors tenen un llibre sobre pi. Després d'haver llegit aquest, crec que va a la llista de llibres per llegir. I amb això crec que ja ho he dit tot :-)
Al principi ho demostra tot, després hi ha algun resultat que no demostra (i que no li hagués costat gaire, per no deixar amb les ganes al personal). Però és rigorós i bastant complet.
Com sempre passa amb els nombres de Fibonacci (o més aviat amb el nombre auri), hi ha moments en què sembla que el vulguin fer entrar amb calçador a tot arreu i que hagi de sortir-hi per força, però a banda d'això, la resta m'ha semblat molt bona.
Ara acabo de veure que els mateixos autors tenen un llibre sobre pi. Després d'haver llegit aquest, crec que va a la llista de llibres per llegir. I amb això crec que ja ho he dit tot :-)
April 26, 2020
This turned out to be a difficult read when it was expected to be a fun romp through one (very important) branch of mathematics. Based on the write-ups, I had expected to be able to follow along with the theory of Fibonacci numbers, and then dive into the joy of its application across the spectrum. Instead, I kept getting bogged down with proofs and explanations, which is ironic since the author frequently states that the proofs are in Appendices!!! Even the applications were heaped with mathematical theory and proofs.
I am not math dumb, in fact made a career in financial structuring which required a fairly high level of math. Yet, I was many times while reading this book left mired in proofs which started to get annoying.
I am not math dumb, in fact made a career in financial structuring which required a fairly high level of math. Yet, I was many times while reading this book left mired in proofs which started to get annoying.
December 17, 2015
Nice look into the Fibonacci numbers, the first part did a good job explaining the history behind the Fibonacci numbers, as well as explaining the relationship with Pascal's triangle, the golden section, and Lucas' numbers.
I did like the fact that the authors stressed that Fibonacci numbers were not found every where (contrary to what other reviews state), and that not all relationships in nature are described by them, and that they were emphasizing the instances in which they do occur. So, it's not your regular crackpot book on Fibonacci numbers.
These authors have other good books on popular math, but this one failed to captivate me. It was not as entertaining as other books I've read. Yes, as many others have mentioned previously you need more than basic math, but not beyond high school math.
The authors intent was to introduce some basic number theory. I would recommend it as a general and gentle intro to number theory.
I did like the fact that the authors stressed that Fibonacci numbers were not found every where (contrary to what other reviews state), and that not all relationships in nature are described by them, and that they were emphasizing the instances in which they do occur. So, it's not your regular crackpot book on Fibonacci numbers.
These authors have other good books on popular math, but this one failed to captivate me. It was not as entertaining as other books I've read. Yes, as many others have mentioned previously you need more than basic math, but not beyond high school math.
The authors intent was to introduce some basic number theory. I would recommend it as a general and gentle intro to number theory.
June 27, 2010
Excellent overview for all things Fibonacci. I read it during a trip to Italy, and made it to his grave, which was not planned, but a nice coincidence. In other words, fairly easy reading.
The first several chapters are key. The rest is a bit lighter. And the authors certinaly are Fibonacci cheerleaders, which was a little annoying to me at times. They hoped to be infectious.
I still personally have problems with putting a golden rectangle over part of a painting and claiming the artist planned it that way. Multiple golden rectangles over all key parts of the painting, I might be more convinced. Don't recall seeing that. But the golden rectangle is certainly pleasing to the eye. So, my money is with the artist stumbling across it.
The first several chapters are key. The rest is a bit lighter. And the authors certinaly are Fibonacci cheerleaders, which was a little annoying to me at times. They hoped to be infectious.
I still personally have problems with putting a golden rectangle over part of a painting and claiming the artist planned it that way. Multiple golden rectangles over all key parts of the painting, I might be more convinced. Don't recall seeing that. But the golden rectangle is certainly pleasing to the eye. So, my money is with the artist stumbling across it.
December 28, 2010
I couldn't get past page 30 and I am a math person! I found the book boring and missing many justification for what the author was looking at. Though the proofs are in the back of the book, they are not detailed enough unless you are fluent in number theory (and then they are obvious). I didn't read far enough to see if Posamentier talked about all of the numbers in nature that are NOT Fibonacci numbers. (selective omission?) While the series is interesting, I think you can find patterns and meaning in just about anything if you try hard enough, e.g. Bible code, Nostradamus, Mayan astronomy.....I suggest a book about fractals instead!
September 7, 2015
I’ve read a lot of books on Fibonacci numbers, the Golden Ratio, and the mathematical constant phi, and this is book offers a good summary of what is known. The chapter on Fibonacci numbers in nature is a good summary, about what you would expect, but the chapter on Fibonacci numbers in art and architecture is one of the best I’ve seen. The chapter on fractals is good and not common in these books. Some of the math is beyond most laymen (and me) but I guess if you are reading this book you are into math in the first place!
October 2, 2008
Independent study
February 5, 2009
Here's a fascinating read about a character we hardly know, even though his name is famous.
January 15, 2010
"The fascinating Fibonacci series"
March 16, 2013
Amazingly inspiring and wonderfully eye-opening. Math showing the wonders of God's creation.
December 1, 2013
Really engaging and thought-provoking.
December 10, 2014
Lots of examples of places this natural pattern of numbers occurs. Plenty of ways to make this part of an enriching math class.
July 30, 2016
It's not really the fault of the book that I didn't understand all the equations!!
But the demonstrations in nature are astounding.
But the demonstrations in nature are astounding.
September 13, 2008
Interesting --but I think you really have to be into math to love this book.
May 30, 2011
Very good. Amazing in how many places those darn numbers can show up.
Displaying 1 - 21 of 21 reviews