Fibonacci'nin İzinde: Dünyayı Değiştiren Unutulmuş Matematik Dehasını Yeniden Keşfetmek

by Keith Devlin, Ezgi Yüksel (Translator)

Modern dünyamız matematik, özel olarak da kalkülüs üzerinde ayakta durur. Kalkülüs inanılmaz güçlüdür. Aya insan indirmek için gereken denklemleri formüle dökmeye ve çözmeye yarayan matematiksel alettir. Bir o kadar da gizemlidir. Modern matematiğin ve kalkülüsün dönüm noktasıysa 13. yüzyılda İtalyan matematikçi Leonardo Fibonacci’dir. Leonard Euler, Karl Friedrich Gauss, Pierre de Fermat’dan Kurt Gödel’e kadar kendisinden sonra gelen bütün matematik dehalarının, temel aldıkları matematik 13. yüzyılda şekillenmiştir. İşte bu macerayı tarihsel çerçevesi içinde ele alan yazarın kendisi de ünlü bir matematikçi. Yazdığı 35 kitap ve yapımcılığını üstlendiği çok sayıda radyo programıyla “Matematikçi Adam” olarak tanınan Keith Devlin bu kitabında okurları tarihsel bir yolculuğa çıkararak günümüz matematiğinin temellerinin atıldığı 13. yüzyılı ve özellikle de Leonardo Fibonacci’yi tanıtıyor.

“Fibonacci’nin İzinde sadece Pisalı Leonardo’nun değil, aynı zamanda matematiğin dünyamızı nasıl şekillendirdiğinin de hikâyesi.”
–MAA Reviews

“Bu kitap Fibonacci’nin Batı kültüründeki etkisini gözler önüne seriyor.”
–Dan Friedman, Los Angeles Review of Books

“Çok rahat okunan, heyecan verici, zamanın ruhunu yansıtan bir kitap.”
–Owen Toller, Mathematical Gazette

“Herkese önerebileceğimiz bir kitap.”
–Adhemar Bultheel, European Mathematical Society

Genres: History, Nonfiction, Science, Mathematics, Biography, Medieval, History Of Science

260 pages, Paperback

First published January 1, 2011

About the author

Dr. Keith Devlin is a co-founder and Executive Director of the university's H-STAR institute, a Consulting Professor in the Department of Mathematics, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 26 books and over 80 published research articles. Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. He is "the Math Guy" on National Public Radio.

Reviews

[Michael Kotsarinis]

Παρουσιάζει όσα γνωρίζουμε για τον Φιμπονάτσι και το έργο του, που έφερε τους σύγχρονους αριθμούς και τρόπους υπολογισμού στην Ευρώπη. Αρκετά περιεκτικό με αναλυτική κάλυψη της σχετικής έρευνας. Βέβαια πρέπει να ενδιαφέρεται κανείς σε μεγάλο βαθμό για την ιστορία των μαθηματικών για να το συστήσω.

[James · Rating 5 out of 5]

I had wanted to write this book. It needed to be written, because the Man of Numbers, Leonardo of Pisa - better known as Fibonacci - was one of the greatest mathematicians of the Middle Ages. We all use the Hindu-Arabic numeral system which he introduced and popularized c. 1200. Fibonacci is most famous for the sequence of numbers named for him, a sequence which is the solution to a story problem that he included in his seminal textbook Liber Abaci to give his readers practice with this 'new' number system. But despite all that we owe to him, Leonardo's story had not been told. That is, not until Keith Devlin came along and told it. And Devlin did it right. In this book we have all the available biographical details about Leonardo Pisano - his accomplishments, sources, and background information - to bring to life this under-recognized mathematical hero.

As I said, I had wanted to write this book. I had obtained a copy of the Liber Abaci. I had been studying Italian in preparation for a trip to Leonardo's locales. I had been reading other biographies about similar men to get a feel for what a good biography is. But that's all over now. I don't need to write anything. Everything that I had wanted to write, Devlin has written. And he did it better than I could have.

I guess I'll take a trip to Hawaii instead.

[Márcio · Rating 3 out of 5]

Even though the basis of our mathematic knowledge, especially the numbers we use today derives from the Arab world, and much of it also derived from the Indians, it was thanks to Leonardo of Pisa (better known today as Fibonacci) who assembled arithmetic knowledge into a book to help merchants do their account with much easiness, that it was spread in the western world. It is an interesting book, though a bit repetitive sometimes.

[Becca]

Dnf at page 60. I only know the very basics of algebra. I'll come back to this book next year when I know more about making and solving equations so I can work out all the fun sample problems.

[Saleh MoonWalker · Rating 3 out of 5]

داستان جذابی در مورد زندگی فیبوناچی بود. توضیح طولانی ولی جذابی راجع به ریشه تحصیلات ریاضی و اولین استفاده سیستم عدد هندی-عربی در اروپا میده. سیستم روایتیش خطیه واسه همین بیشتر برای کسانی که به ریاضیات علاقه مند هستن جذابه.

[Bill Kubeck · Rating 4 out of 5]

Often the person who has the greatest impact on society is not the person who invents or discovers a great idea, but the one who is able to explain it to a broad audience. This is the case with Leonardo Pisano. He didn't invent anything because you don't invent in mathematics, and he didn't discover anything new. But he knew that the rapid growth of business and trade demanded a better way of calculation. Thus he wrote Liber Abbaci, a manuscript filled with practical examples of real use of the Hindu-Arabic number system. This the primary source for hundreds of calculation books written in the next two centuries, books that taught generations of traders and bankers a better way to reckon business.

Much has been written of Leonardo's mathematics. Less has been written of his history. And given the miserable difficulty of this kind of historic research, few realized that the evidence was there to finally prove that Liber Abbaci was the source of the later books. Devlin's contribution here is to carefully assemble all the evidence to give us that proof.

[Annie · Rating 3 out of 5]

This was definitely an interesting read. At 150 pages, it was just the right length to learn about the man who introduced the Hindu-Arabic number system to the western world. Without his practical instructions, the advances in the western civilization definitely would have been delayed.
This was also a very educational read. I learned many facts about Fibonacci that I didn't know or wouldn't know to ask. Such as Fibonacci is not his real name, it's Leonardo (another talented Italian Leonardo). Or that he's from Pisa (just like Galileo Galilei). Or that this Lenardo didn't invent anything per se, but made a new and difficult concept palatable for the masses. Many of these facts are trivial, but someone who loves random knowledge, it is a worthwhile read.
I wished the book delve more into his famous numbers sequence, but the book is titled The Man of Numbers. I will have to go read up on the Fibonacci sequence in another book.

[Bob Gustafson · Rating 3 out of 5]

This biography, kind of, is like the one I recently read of Eratosthenes. In both cases it seems to me that the authors did boatloads of research, came up nearly empty-handed, but had to produce something to justify the work they had done. So there are a bunch of interesting facts about Pisa, about the states of math and commerce in thirteenth century "Italy" and about Indian contributions to mathematics, and a few about Leonardo of Pisa.

[Kili · Rating 3 out of 5]

All computer science students know Fibonacci numbers: F(1) = F(2) = 1, n > 2: F(n) = F(n-1) + F(n-2). Remembering Fibonacci for this series is much like people in 2816 calling the hypertext abstraction Job text. That's not exactly right - the people in 2816 would also have to think that Steve Job's name was Appledad.

Fibonacci was named Leonardo, and came from Pisa, hence his name in his time would have been "Leonardo Pisano" (Leonard from Pisa). The name "Fibonacci" comes from "Filius Bonaccio" - eg, the Bonaccio Family - which is perhaps the name of his Grandfather.

I especially enjoyed the view this book gave into the state of European mathematics at the beginning of the 1200's. Roman numerals aren't that hard for addition or subtraction (I didn't know that) - it's multiplication and division that is difficult with them. There were elaborate methods of computation that used fingers, and the Europeans of his era had their own kind of abacus (different from the Chinese one). Leonardo introduced to a broad public not only "Arabic" numerals, but also the algorithms we use to multiply and divide with them - as well as methods for computing square roots, cubic roots, and approaches for many kinds of practical problems. His book Liber Abbaci was scholarly, but it caught on and revolutionized the way merchants computed. His role was not unlike Steve Jobs or Bill Gates - taking known technology and making it available for the people who could take practical advantage of it. The book that did this was titled Liber Abbaci.

Leonardo wrote many books in his time, and was hugely influential in many kinds of mathematics. He was widely recognized for his role, but when books started to be printed, his own books (hand copied and thus relatively rare rare) became less important.

Then again, does the common person remember Brahmagupta as the first person to give the rules for the mathematical properties of 0? He is the person who first wrote rules like 0*x = 0, and 0 - x has the opposite sign of x. He did say that 0/0 = 0, but Newton and his science of infitesimals was a thousand years in the future. This was a revolutionary discovery of the 600s - a fact I also learned from this book.

Fibonacci numbers are an example that Lorenzo included in Liber Abbaci. From that book:

HOW MANY PAIRS OF RABBITS ARE CREATED BY ONE PAIR IN A YEAR

A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear another.

---
At first, this sounded like an exponential series to me, but the key is that it takes a month for rabbits to become fertile. So, if the number of pairs of rabbits at month n is the number of pairs of rabbits at month n-1 (none died) plus the number of pairs rabbits at month n-2 (these are all now fertile).

I wish the book had been longer - some of the text is too terse to fully appreciate. For example, Devlin describes the occurrence of Fibonacci numbers in nature (eg, the number of petals on a flower is almost always a Fibonacci number). I learned why this is the case in another book (that I'm reading now).

[Pete Wung · Rating 3 out of 5]

I will have to admit, this is not what I expected. Kevin Devlin has gained popularity as a proselytizer of mathematics, and this book on Fibonacci seems to be the perfect vehicle for someone as erudite and learned in the mathematical arts as Devlin. But this book was a disappointment.

I do not attribute it all to Devlin however. He chose a very difficult and hardly simple task. As Devlin himself admitted, there is scant history on Fibonacci the man, let alone his mathematics. Devlin must have had a devil of a time gaining proper perspective on the man's life and his ability as a mathematician. He has had to depend on mostly tertiary sources and a very active imagination to tell the story.

In addition, the main contributions of which Devlin is writing about: the importance of the Arabic number system on the evolution of western commerce and science is something that we take for granted. the idea of how to represent numbers is such a large part of our DNA that the discussions, very well crafted discussions, seem to be obvious and rather a waste of breath. It is of course anything but a waste of breath, but it just seems that way.

The other major issue is that Fibonacci was not the originator of the number system, he was the popularizer through his writings. And popularizers rarely get the respect that originators get.

Lastly, Devlin is a mathematician, his attempt at history writing is admirable but not entirely rigorous nor is his writing of the history riveting. The mathematics was quite well written, but the history part was less than satisfying, partly due to the lack of original material on which to base the story on, and partly because the historical writing seem to be pedestrian and somewhat rushed.

I have to hand it to Prof. Devlin for giving it the old college try, and there seems to be quite a bit of hard work and scholarship involved, it just wasn't a mathematical nor a history page turner.

[Koen Crolla · Rating 4 out of 5]

Leonardo of Pisa, more commonly known as the guy who is more commonly known as Fibonacci, revolutionised popular acceptance of applied mathematics through his Liber Abbaci, which also helped bring the Hindu-Arabic numeral system to the West. Precisely because he was so successful, the full extent of his influence has been greatly underestimated, and his revolution was largely forgotten for hundreds of years. This book aims to right this wrong by examining what it was Leonardo did and how his work was received.

I've previously favourably reviewed Devlin's Mathematics: The New Golden Age (though the review itself seems to have been lost in the move between book-reviewing websites); The Man of Numbers is more modest in scope than that book, though it accomplishes what it sets out to do just as well.
It is, of course, a popular history of mathematics written by a mathematician, with all the sloppiness and inaccuracy that entails, but it's more than acceptable if you read it for the general idea rather than any of the specific details; the point is to inform people that there was more to Fibonacci than his numbers, and the book accomplishes that adequately.

[Vicki Cline · Rating 5 out of 5]

This was a really interesting book, which cleared up a lot of misconceptions I had about Fibonacci. I had thought his main contribution to math was his series (1, 1, 2, 3, 5, 8, ...), where each new element is the sum of the previous two, and which is found in many places in nature. I had thought he lived in the 17th or 18th century, and that his name was Fibonacci. Actually he lived from around 1170 to 1250, his name was Leonardo Pisano (Leonardo of Pisa) and his real claim to fame was the popularization of the Hindu-Arabic numeral system in medieval Europe. Until his book Liber Abaci (Book of Calculation) became widely circulated, merchants used Roman numerals and abacus-like counting boards to do their calculations. One interesting feature of the book is that the ten chapters are numbered from zero to nine. It's amazing to think how cumbersome simple arithmetic was without zero and using only Roman numerals.

[Tim · Rating 4 out of 5]

Fascinating short book about the life of Fibonacci, the man who brought numerals to the Western world. Devlin explains how mathematical innovations from China, India and Arabia transported to Northern Africa where Fibonacci found them while working as a merchant. Devlin does a great job of explaining the history of mathematics, though I wish he could add more detail but I suspect a lot of the historical record is missing many details.
The amazing point to me was how this was in the days before Algebra, so Fibonacci had to write our the problems in words - just like in 3rd grade. He wrote a workbook with scores of examples - all in words! I think it is fascinating how Fibonacci wrote not a work of mathematical theory but an exhaustive list of examples of algebra. He argued for use of numerals not through the universities, but through the practical advantage it gave merchants.

[Conor · Rating 1 out of 5]

What should I say about this one?

How about: This is not a book, it's an essay that was pushed far beyond its means. What's worse, the essay part lacks an effective argument.

Or: This is equal parts down-talking, back-tracking, bush-beating-around, and essay.

Or even: The total effect of reading this might be less effective and educational than reading the page on Wikipedia for Fibonacci.

Or maybe: I got this free, if I had to pay the $25 cover price for it, I'd be absolutely livid. I mean, I get it, the guy researched a difficult topic, came up with nothing, and still decided that he needed to write a book. $25 is too steep for a book that lacks more than it has.

Anyway you choose, I've got nothing nice to say about this one.

[Dolly · Rating 3 out of 5]

I received this book for free through Goodreads Giveaways. It's a fascinating look at the life of Leonardo Pisano, otherwise known as Fibonacci. It has a lengthy discussion of the origins of mathematics education and the first usage of Hindu-Arabic numerals in Europe. The narrative isn't overly exciting, but it's a quick read and would interest anyone who enjoys math. I liked the story and learned a lot about the beginnings of math as we know it today.

new words: incommensurable, portolan

[Nick · Rating 4 out of 5]

By the turn of the first millennium, the Hindu-Arabic numerals we use every day were well established. However, Europeans remained wedded to Roman numerals, unwieldy and ill-suited to arithmetic as they were. The man we now call Fibonacci, known in his own time as Leonardo of Pisa, appears to have been responsible for popularising the 'new' numerals via his seminal work, Liber abbaci ('The book of calculation'), completed in 1202. But despite what seems to us to be their self-evident superiority, use of the Hindu-Arabic numerals still spread slowly among the population. As with any innovation, many were suspicious, pointing out that the new numerals made it easier to falsify documents by, for example, changing a '6' to a '9'. Roman numerals took preference in Italian law. Resistance continued throughout the thirteenth, fourteenth and even fifteenth centuries. Perhaps we should not be too surprised by this, given the continuing resistance to metricisation in a far more globalised world.

What fascinates Devlin is how Leonardo formed the bridge by which Hindu-Arabic numbers crossed from East to West. We know frustratingly little about his life, but Devlin makes a convincing case for his historical importance, showing how his mathematical works were unusually thorough, detailed and brilliant (even if not wholly original) and were relied on heavily by later scholars. The Fibonacci sequence for which Leonardo is known today (which again, he did not invent) is a fairly minor detail of Liber abbaci, a whimsical problem inserted as a diversion and perhaps a way to practice using the new numerals. More importantly, Liber abbaci is a demonstration of the usefulness of the Arabic numbers in performing calculations and solving a large variety of problems (many with practical applications).

Devlin presents several of these problems in the book, and shows how Leonardo solved them. Impressively, he did this without the help of modern notational algebra, so that solutions are spelled out rhetorically, with words such as "res" standing for unknown quantities. Here is a sample: "Therefore if you add: the total store minus two res and half the store minus one and a half res and one-fifth the store minus one and one-fifth res, the total amount, the sum of the amounts the three men took, equals one and seven-tenths of the money minus four and seven-tenths res." The sheer mental effort required to follow this sort of stuff, compared with a modern symbolic representation, seems enormous.

This book offers an interesting insight into an episode of history that is very little thought about. For Europeans, the introduction of modern numbers was not a great leap forward, but a gradual process that seems in retrospect painfully slow. But it took someone like Leonardo of Pisa to set that process in motion. The aim of this book is to restore Leonardo to what Devlin sees as his rightful place alongside the likes of Galileo (a fellow citizen of Pisa), Copernicus and Kepler. Devlin certainly succeeds in arguing for his prime importance as a visionary teacher and communicator.

[Fred Cheyunski · Rating 4 out of 5]

Concise Story of Modern Arithmetic/Business Expansion Origins - This book on Leonardo of Pisa, or Fibonacci as he was also called, offers background, antecedents, and implications of his Liber Abacci (written in 1202) that helped popularize and spread the use of Hindu/Arabic numbers in the West.

The author, Keith Devlin, introduces the reader to Leonardo’s upbringing and exposure to these numbers through his accountant/trader father in Italy and northern Africa. He also gives us interesting tid bits such as that al-Khwarizmi’s manuscripts (e.g. Algoritmi de Numero Indorum) in the 9th century served as sources for the Hindu/Arabic computations that Fibonacci’s text incorporates (his name gave rise to the modern word “algorithm”).

Devlin compares Leonardo’s writing to the introduction of the personal computer in terms of its revolutionary affect in the 1980’s. He goes to lay out the effects of Hindu/Arabic number use such as related to the development of the portolan chart/navigational map (i.e. detailing ports and harbors) and financial accounting as in the Medici bank ( as early as 1232) that drastically changed how business was done in the 13th century. The expanded use of the abacus book and abacus schools helped lead to Italian commercial enterprises having global reach and widespread influence by the end of the 14th century. By the end of 16th century all of Europe was using the Hindo/Arabic numeral system which underpinned the continued advance of commerce and science.

As in his “The Unfinished Game” (about the correspondence between Pascal and Fermat that helped solidify the basis for probability and statistics and industries such as Insurance and Finance), Devlin, in "The Man of Numbers," beautifully and concisely tells us the story of the origins of our modern arithmetic and business expansion. Pick up this book for an enjoyable and informative read.

[George Girton · Rating 4 out of 5]

A unique classic that I stumbled across in a used bookstore, and am now enjoying again as an audio book . Word problems, practical algebra and step by step fractional math problems circa 1200. I gave copies to pals of mine who were bereft of computational reading materials and also read Devlin’s sequel book on his research in this one.

In the sequel Devlin walks into a public library somewhere in Italy (a mathematician walks into a library) and says “you wouldn’t happen to have a copy of Fibonacci s book Liber Abbaci, would you?” And they bring him this 600 page book that’s 600 years old.

With its overload of detailed math problems Man of Numbers does not make a terrific audio book but I’m getting huge enjoyment from it.

[Viewpoints Radio · Rating 5 out of 5]

As hard as it is to imagine, before an Italian mathematician we know as Fibonacci came to the scene, most people didn’t use… numbers. Keith J. Delvin dives into this man's life and how he tremendously helped shape history as we know it. We had the chance to speak with Delvin about Fibonacci's significant contribution to mathematics and our daily lives. To hear his interview, check out our radio show Viewpoints Radio! For the full story, check out this LINK: https://viewpointsradio.wordpress.com...

[Duane · Rating 1 out of 5]

This was clunky. I was hoping to be fascinated by the story of the how Fibonacci inoculated the western world with Arabic numerals and changed everything forever. Which he did, the problem was the author had so little biographical data to go on that he admitted that everything was pretty much a guess. Not sure where he was born, know he lived in Pisa. He wrote a book on arabic numerals. Oh, and he mentioned a problem that had an interesting sequence, that other people already knew. I was hoping for more.

[Lynn · Rating 5 out of 5]

I first encountered Fibonacci and his wonderful numeric sequence in The Book of Lost Names by Kristin Harmel. I had never heard of him or his numbers, and, when I asked around, neither had anyone else. I did some Googling, and found that he was indeed a real person.

I was excited to find this small book which details his life, his introduction of the number system that we know today, and, of course, his marvelous Fibonacci numbers.

Read it and prepare to be amazed!

Library book published by Walker & Company, 2011

[Emily Sharpe · Rating 3 out of 5]

Good book. I really enjoyed digging into some of the mathematics discussed. It was challenging to picture math in the way that Leonardo of Pisa did, as ours is so different today. I felt the book was at times a little boring and had a few errors (i.e., listing three as tres in French and tre in Spanish, when it should be trois and tres, respectively), but overall was an interesting look at a little known figure. I did also like the ability to see into other lesser known mathematical figures (at least, lesser known to the layperson).

[Thomas · Rating 2 out of 5]

Meh. This could have been a brief essay to correct the common understanding of why Fibonacci is important in the history of math. Instead, it was a all too long and largely boring droning on about unnecessary details. This includes fun facts like listing all the chapter titles for various books (I don't even remember why they were important -- I was just struggling to keep listening by this point).

[Nancy · Rating 3 out of 5]

So why did it take me 4 months to read this book which 158 pages not counting the notes at the end? Basically it is a book about the origins of modern arithmetic with a lot of word problems aimed at 13th century merchants. The plot itself is very thin as not much is actually known about Fibonacci the man. Nonetheless, occasionally I was in the mood to read about these math problems and play with them myself. Kind of fun in a geeky sort of way.

[Jim Lyons · Rating 4 out of 5]

Fascinating history of Leonardo of Pisa (aka Fibonacci), who brought modern numbers and their business applications to the Western world. It is a relatively short book, though I got bogged down in the middle, in part due to a European trip which included a stop in Pisa and the statue as pictured in this book. I am happy to have finally finished it, especially since the final chapter contains a fine summary of the Fibonacci sequence and the related Golden Triangle.

[Ioannis Apostolopoulos · Rating 5 out of 5]

Ένα καταπληκτικό βιβλίο που διαβάστηκε απνευστί για έναν άνθρωπο μεγαλοφυή που με το έργο του Liber Abbaci του 1202,διαμόρφωσε τον σημερινό κόσμο αλλά και τον σημερινό άνθρωπο,έναν άνθρωπο που βρισκόταν πολύ μπροστά από την εποχή του αλλά ταυτόχρονα ζούσε μέσα σ´αυτή. Αυτός είναι ο Λεονάρντο της Πίζας γνωστός με το παρατσούκλι που του κόλλησαν τον 19ο αιώνα Fibonacci!! Ο Λεονάρντο Πιζάνο δικαιούται να σταθεί δίπλα σε ένα Αρχιμήδη , Κοπέρνικο,Γαλιλαίο , Κέπλερ,Νεύτωνα και Αϊνστάιν!!

[Sean Reeves · Rating 3 out of 5]

The book is about the "arithmetic revolution" that Fibonacci helped create through his published works and it's interesting enough. There is very little said about the man himself because very little is known. The title should have been "Fibonacci's Arithmetic Revolution" without "The Man of Numbers" preceding it, the latter implying that it's a biography which it really isn't.

[Andrew Davis · Rating 3 out of 5]

A brief account of life of Leonardo of Pisa (later called Fibonacci) and his book “Liber abbaci”, that introduced the Hindu–Arabic numeral system in the Western World. The book has been published in 1202. Very little is known about his life and the book attempts to combine the few known facts with the social environment of the times.

[Teri L. · Rating 3 out of 5]

Not sure why I had this book on my bookshelf. A gift perhaps? I skipped over some of the descriptions of solving math problems and focused on the history of Pisa in the 1200’s and the biography. Math nerds would probably enjoy the story of how the world came to use the Hindu-Arabic system of 10 digits we use today.

[Ted · Rating 3 out of 5]

Fibonacci was from Pisa and in the 1200s he wrote a famous text showing how to do math with the hindu-arabic numbers. He built on the work of middle eastern men that wasn't used in Europe at the time. It is short, and good for those who are interested in how things we take for granted today came to be.