Review 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.

Update: Giveaways are over. Congratulations to the winners!

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.

Keith Devlin
Fibonacci’s ‘Numbers’: The Man Behind The Math
excerpt from The Man of Numbers

* 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.

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.

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

Gregor Reisch: Madame Arithmatica, 1508

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.

Keith Devlin
Leonardo and Steve, Kindle locations 258-261

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.

Keith Devlin
Leonardo and Steve, Kindle Locations 378-393

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.

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?

If you don’t win the giveaway, Leonardo & Steve is available at Barnes & Noble or Amazon or Smashwords for a mere $2.99. Keith would like to hear your reaction to the book:

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.

Keith Devlin
Author comment on Leonardo and Steve
[Keith’s name above is an email link, or you can find his email address here.]

32 thoughts on “Review and Fibonacci Puzzle

  1. Hi, I love using literature to peak the interest of children and gently encourage them to discover theories and truths with a little guidance! One of our favorite books when my children were young was “Ben and Me, An Astonishing Life of Benjamin Franklin As Told By His Good Mouse Amos” – written by Robert Lawson. What a wonderful way to blend literature, history, science, and fun! Although my children are grown I am now homeschooling my grandson and I plan to continue encouraging the exploration of great books such as this one!

  2. I was able to turn around a math hater using math biographies. We enjoyed Mathematicians Are People Too as well as Carry On Mr Bowditch. Mr Bowditch is a great example of what you can learn when you make the choice to keep learning no matter what your circumstances. Thanks for offering the ebooks!

  3. As a student, I had no time for the history of mathematics, or for biographies of mathematicians. I just loved the mathematics and did not care who had discovered/invented it or when. Most (all?) of my fellow math students felt the same. But faced with teaching mathematics to nonscience majors at university, I soon discovered it was a great way to draw them in. I’ve been using that hook ever since.

  4. My kids are still kind of young and we have only been doing MathStart and other books of that nature. I am looking into which math history book would be a good one to start of reading to them though.

  5. I enjoyed reading Number, the Language of Science by Tobias Dantzig. It gives a nice overview of how various branches of mathematics developed, and chronicles mathematical developments from prehistoric to modern times. The book is for adult or teenage readers.

  6. I have a 10 year old daughter who loves history (and science) but doesn’t have anything good to say about math. I keep trying to convince her that math can be interesting and fun, so this year I’d like to introduce more of the history of math and have her play around with cool concepts like the Fibonacci sequence.

    Thanks for giving me a place to start.

  7. I do not yet have a favorite resource. I continually look for things that will interest my children while learning. I have found the ideas and posts of others to be good ideas of things to try in our own family.

    Thank you.

  8. I have not used math history to teach math, but the more I’m learning about math history, I would really like to. This book sounds awesome!

    Thanks for sharing & hosting the giveaway!

  9. We use lots of maths history – currently using “Mathematicians are people too”. We enjoy Theoni Pappas’ books also. Had lots of fun with Fibonnacci… shown here on our homeschool family life blog
    I think maths history is a great way to talk about invention, discoveries and concepts in maths in a different way from plain old formulas and worksheets. Its living maths!

  10. I use lots picture books to teach math concepts during the year. No matter how old kids always love to hear a story.

    My two favorites are:

    Sir Cumference and the First Round Table (A Math Adventure) by Cindy Neuschwander
    How much in a Million by David M. Schwartz

  11. What a delight it would be to share this with my children. I haven’t used much history to teach math, but I’ve used dozens of picture books to explore concepts, like Sir Cumference, or the 100 Ants. Great stories that explore math concepts in a different way. I’d love to start seeing and learning the history myself and sharing that with my kiddos.

  12. I read Carry On, Mr. Bowditch to my oldest and intend to read it again to my younger ones soon. I have had my oldest son read some biographies of scientists that contained lots of math, too. I want to integrate more math history. I have read many MathStart books to my kids. I like Greg Tang’s math books, too. I know they’re not exactly Math history, but they do present math in a palatable way to my children who tend, for the most part to be Math-phobic.

  13. Hi, I use a lot of Vedic maths to help me son with quick maths. He loves being fast. Constructing long stories which uses addition, subtraction, division, multiplication, fractions and decimals is something I strated recently. I let him construct the story and then correct it so that he solves them correctly. In the due course he will have to solve it and let me know the answer. These days we go jogging in the evening and we keep doing basic functions with the door numbers, which is the greatest and the least numbers we saw today etc.
    Sooooo much of summer fuuuuun.

  14. I have a reader that doesn’t like math. Using books to encourage her in math has just come to my attention and a few of the books that I plan on using this year are the Sir Cumference series, Mathematicians are People Too, Real Life Math Mysteries, A Place for Zero, and Multiplying Menace. I hope this helps her as well as my 3 other kids.

  15. I never actually thought about using math history as a way to encourage my kids to fall in love with math. (Who can fall in love with page after page of the same type of equations…?)The boredom of repetition is discouraging… I will definately be bringing this to their attention. Thanks.

  16. We love math picture books here at my house. We haven’t started math history yet. I love math and haven’t ever read the history of math but am so excited about teaching this to my kids. We are going to read Mathematicians are People Too this year.

  17. I attempt to provide students some background information (a historical perspective) on various topics that are part of our curriculum in Ohio.

  18. We homeschool using the Charlotte Mason philosophy, which is heavy on living books that delve deep into their subject for a more thorough introduction. This would fit perfect! Thanks!

  19. Would love to get a copy of this book. My 10 year old has struggled with math for a while and hoping he will “get it” this year. Imagine this would help. Thanks!

  20. Honestly, I’m sorry to say that the only math history I’ve ever encountered or taught to my little man was that which was brought up in RightStart Math by Dr. Joan A. Cotter. We learned about Hindu-Arabic numbers vs. Roman Numerals. Until Maria Miller of Math Mammoth linked your blog, I’d not thought much more about teaching math history. Now, my curiosity is piqued and I must explore this further! I hope we win a copy of the e-book Leonardo & Steve!

  21. Anno’s Magic Seed is one of our favorites. We’ve also started reading Mathematicians Are People, Too, and it’s one I think we’ll read again and again on multiple levels. This book about Leonardo would be fascinating addition to our home. Thank you.

  22. My favorite math story would be hard to pin down, but for sure Potok’s “The Chosen” is on the short list. And call me strange, but for me C.S. Lewis reads very mathematically. The way he develops an idea is almost like long division, where he “carries” a thought for a while and then brings it in at a higher magnitude of argument in order to reflect the principles (values) more accurately.

    As for how I teach math: I have kids ranging from 20 down to 5, and keeping their educational needs in my head, where they intersect, where they differ, is quite a grouping “problem”. The order of operations is constantly being challenged, and the commutative and associative principles are definitely in play.

    I like to use critical thinking and logic as we discuss literature and poetry; I like to ask “math-based” questions as a bridge to correlation of disciplines, like going from music to physics, history to geography, science to biography, etc. I could go on, of course, but I imagine I would lose your interest.

    Rachel DeMille

  23. I love “Carry On, Mr. Bowditch”. I had to read it for a class I was taking and found it to be fun and inspiring. I will be reading that to my kids this school year.

  24. I use a set of book on the History of Mathematics and pull out the nuggets that I think will excite my students. I can’t quote the author right now since my classroom is just in the stage of being unpacked for the next year. I look forward to checking out more suggestions above.

  25. As a long time math teacher, I have always believed in the integration of math and literature. I know it opens the door for students with differing learning styles. It can also take away some of the ‘intimdation’ that can be associated with ‘doing math problems.’ Anyway, I created a website:
    (it’s free) for teachers, homeschoolers, and students that has many of the resources I have created.


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