Sunday, October 21, is the worldwide hexaflexagon party in honor of Martin Gardner’s birthday. Gardner’s article about hexaflexagons launched his career as a recreational math guru who inspired people all around the world to love math.
I’ve been enjoying the Introduction to Mathematical Thinking course by Keith Devlin. For the first few weeks, we mostly talked about language, especially the language of logical thinking. This week, we started working on proofs.
For a bit of fun, the professor emailed a link to this video. My daughter Kitten enjoyed it, and I hope you do, too.
Who Killed Professor X? is a work of fiction based on actual incidents, and its heroes are real people who left their mark on the history of mathematics. The murder takes place in Paris in 1900, and the suspects are the greatest mathematicians of all time. Each suspect’s statement to the police leads to a mathematical problem, the solution of which requires some knowledge of secondary-school mathematics. But you don’t have to solve the puzzles in order to enjoy the book.
Fourteen pages of endnote biographies explain which parts of the mystery are true, which details are fictional, and which are both (true incidents slightly modified for the sake of the story).
I ordered Who Killed Professor X? from The Book Depository (free shipping worldwide!), and it only took 5 days to arrive here in the middle of the Midwest. My daughter Kitten, voracious as always, devoured it in one sitting — and even though she hasn’t studied high school geometry yet, she was able to work a couple of the problems.
In 1905, when he was 26 years old, Albert Einstein rocked the scientific world with a series of papers that changed our understanding of the nature of the universe. At MinutePhysics, the celebration continues:
March 14th is Pi Day, and it’s also Albert Einstein’s birthday. In honor of Einstein, MinutePhysics is posting a series of videos on his “wonder year” of 1905, when he published several papers that eventually earned him the Nobel Prize.
Homeschooling is much more than just doing school at home — it’s a lifelong lifestyle of learning. And thanks to the modern miracle of inter-library loan, even those of us who live in the middle of nowhere can get just about any book sent directly to our tiny home-town libraries.
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.
* 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
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.
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.
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.
And that’s only the beginning. Below, I’ve listed a wide variety of math-related links collected from past samplers. Though be warned: Dover does change its website from time to time, so these pages may disappear without notice.