Review/Giveaway and Fibonacci Puzzle
Thanks to author Keith Devlin’s generosity, I am giving away FIVE copies of his new e-book Leonardo and Steve: The Young Genius Who Beat Apple to Market by 800 Years (at the end of this review post), PLUS a signed copy of his latest print book, The Man of Numbers: Fibonacci’s Arithmetic Revolution.
What Leonardo did was every bit as revolutionary as the personal computer pioneers who in the 1980s took computing from a small group of “computer types” and made computers available to, and usable by, anyone. Like them, most of the credit for inventing and developing the methods Leonardo described in Liber Abbaci* goes to others, in particular Indian and Arabic scholars over many centuries. Leonardo’s role was to “package” and “sell” the new methods to the world.
The appearance of Leonardo’s book not only prepared the stage for the development of modern (symbolic) algebra, and hence modern mathematics, it also marked the beginning of the modern financial system and the way of doing business that depends on sophisticated banking methods.
* Leonardo of Pisa, also known as Fibonacci, used two b’s in the word “calculation” (abbaci) to distinguish his methods from the use of an abacus.
Can You Solve This Fibonacci Puzzle?
If you want a chance to win a personally signed copy of The Man of Numbers: Fibonacci’s Arithmetic Revolution, all you have to do is solve this riddle.
Do NOT give your answer as a comment here! If that email link doesn’t work for you, then copy my address by hand: lets play math [no spaces] at gmail dot com.
Here is the puzzle:
The Fibonacci sequence arises in the solution to a problem about a breeding rabbit population that Leonardo gave in Liber Abbaci.
But there is evidence that in another book he gave the problem in terms of different creatures. What were they?
[Hint: The answer is in the e-book, Leonardo & Steve. But this is a no-purchase-necessary contest: There are at least two places to find the answer online, if you search carefully.]
Even if you live outside the U.S., feel free to enter! Keith says he would be happy to ship internationally.
I will accept email answers for two weeks, through Monday, August 15. Then I will gather up all the correct responses, numbered in order of receipt, and use random.org to choose a winner. I will email the winner to get your address, which I’ll send on to Keith so he can mail your book.
Update: I received a wide variety of answers to the Fibonacci riddle, including sheep, mice, donkeys, kittens, chambered nautilus, spiders, cow, dog, fox, sunflowers, humans, and an amoeba. Honeybees were by far the most popular wrong answer. Seven people managed to discover the correct creature. (No, I’m not telling! The answer is in the e-book, and it’s an interesting story to read.) Our official winner is Ken. Congratulations! I’ve sent you an email.
Math History E-book: Leonardo & Steve
When teachers share stories from the history of math, we help students build a mental picture of the ebb and flow of ideas through the centuries: how men and women wrestled with concepts, made mistakes, argued with each other, and gradually developed the knowledge that today we take for granted.
I taught my Math Club to use a medieval counting board, but still I have trouble imagining the historical setting. What was it really like to work and think in Roman numerals, and then to suddenly learn this new way of calculating? In Leonardo & Steve, Keith draws a parallel between Leonardo’s work and the personal computer revolution — and having lived through the latter helps me understand what it was like when the Hindu number system changed the world.
To the reader today, Leonardo’s text describes something we have been familiar with since our early childhood math classes, but at the turn of the thirteenth century, elementary arithmetic was entirely unknown. When Leonardo was writing his mammoth work, the information it contained was as new to him as to his future readers. In many cases he was working out the examples for the first time ever. He was working them out for himself as much as for his later readers.
A Math History Mystery
In addition to the title characters’ stories in Leonardo & Steve, I found the mystery of the abbacus books interesting. These were small math instruction books for the lay reader, like the Treviso Arithmetic. Hundreds, perhaps thousands, of people across Italy published abbacus books (at first handwritten, later printed) in the years after Leonardo wrote Liber Abaci. And then the books disappeared from history, until scholars rediscovered and began to write about them in the 1960s.
The abbacus books were not written by people doing original mathematics, but by people who learned the new way of working with Hindu-Arabic numbers, found it exciting, and wanted to share it with others. [Sort of like math teacher blogs?]
It would have made sense if the abbacus books had been copied from Leonardo’s Liber Abbaci — but they weren’t. So where did this flood of arithmetic books come from? Keith tells a story of historical forensics, as modern-day literary detectives sift clues to find the original source of the abbacus writings.
Despite the fact that medieval authors copied freely from one another all the time, hardly any of the abbacus books contained any passages from Liber Abbaci. The vast majority of abbacus books, including all the known early ones, had almost nothing in common with Leonardo’s masterpiece. Clearly, the authors of those early abbacus books found their material elsewhere than in the dense pages of Liber Abbaci.
How to Enter the E-book Giveaway
For a chance to win a copy of the e-book Leonardo & Steve (in your choice of format), you have two ways to enter the contest:
- Scroll down and leave a comment on this post answering one (or both) of these questions:
What is your favorite math history resource, or favorite math story?
Do you use math history in your teaching — and if so, how?
- Post about this contest on your own blog, tweet about it, or otherwise share the news, and then come here and leave a comment telling me about your link.
You may do both (comment on the questions and link to the giveaway), to double your chances — but please make sure your link is in a separate comment from your answer to the questions, or I may forget to count it separately.
I will accept entries for nearly two weeks: through Monday, August 15. After that, I will count up all the entries (numbered in order of their appearance in the comment section) and go to random.org to generate the five winning numbers. I’ll send the winners’ email addresses to Keith, so he can give you a claim code to download your books.
Update: Omitting the comments by Keith Devlin and the blog carnival pingbacks, we had 34 entries in the e-book giveaway. Congratulations to Judy, Katie, Penney, Rachel, and Charlotte! I will forward your email addresses to Keith, and you should be receiving a download code for your e-book soon. Thank you all for participating!
Would You Buy Math History for the Price of a Latte?
As an author, the short, cheap, e-book format is new to me, and I think this is the first ever popular mathematics e-book. So please let me know what you think. In addition to knowing your views of the content, I’m eager to know your reaction to the format and the price. Many fascinating stories about mathematics can be told in 15,000 words, so if authors like myself can get it right, this could be a major part of the future of popular mathematics writing.