★★★★★ Twenty-five years of recreational mathematics

Hexaflexagons and Other Mathematical Diversions

Martin Gardner

In 1967 my Aunt Althea, the very best of all possible aunts, gave me a subscription to Scientific American for my twelfth birthday. I remined a subscriber until the 1990s. Among the best features of SA were the monthly columns "The Amateur Scientist", where you could learn how to build a laser in your garage -- you think I'm joking, but I'm serious -- and Martin Gardner's Recreational Mathematics column "Mathematical Games". Yes, I know that to many of you the phrase "recreational mathematics" makes about as much sense as "recreational colonoscopy", but there are enough people who were willing to entertain the idea that math could be fun to sustain Gardner's column for 26 years. I was one, and Gardner was brilliant.

These columns were collected and published in fifteen books by SA. The best way to get them now is in electronic form. There is a searchable CD-ROM version, and also the American Mathematical Society will sell you PDFs of all 15 as a package deal. The fifteen books, as numbered by AMS, are

1. Hexaflexagons and Other Mathematical Diversions
2. The Second Scientific American Book of Mathematical Puzzles and Diversions
3. New Mathematical Diversions
4. The Unexpected Hanging and Other Mathematical Diversions
5. Sixth Book of Mathematical Games from Scientific American
6. Mathematical Carnival
7. Mathematical Magic Show
8. Mathematical Circus
9. The Magic Numbers of Dr. Matrix
10. Wheels, Life, and Other Mathematical Amusements
11. Knotted Doughnuts and Other Mathematical Entertainments
12. Time Travel and Other Mathematical Bewilderments
13. Penrose Tiles to Trapdoor Ciphers and the Return of Dr. Matrix
14. Fractal Music, Hypercards & More Mathematical Recreations from Scientific American Magazine
15. The Last Recreations

(Most of The Magic Numbers of Dr. Matrix was originally published as number four in the series, which was later reprinted and expanded, explaining why Sixth Book of Mathematical Games from Scientific American is number five in the AMS numbering.)

There's a lot here. A "Greatest Hits" compilation would be nice. The closest thing to that that I have found is this SA blog post, listing ten of Gardner's best articles. Unfortunately, the links take you to paywalled SA pages. Still, if you have bought the books, it's useful.

Gardner sometimes made the silly claim that he was not a professional mathematician. There is no sensible understanding of the term "professional mathematician" under which this claim is true. I was tempted to write "uncharacteristically silly" in the above sentence, but then I remembered that Gardner was often very silly, for instance in his annual April Fools column. This was a man who was always up for a little fun and knew how to find it.

Gardner's work was revered by professional mathematicians, and Mathematical Games was great in part because they talked to him and told him about their latest work. Some important new math was thus first published in Mathematical Games.

A regular feature of the column was puzzles. I remember this one in particular:

EVE/DID = .TALKTALK...

The puzzle is to assign a distinct digit to each letter (E, V, ..., K) such that the equation is true. The fraction is in lowest terms. The unique solution is

242/303 = .79867986...

As a high-school student I had fun solving that. Gardner published a collection of his best puzzles My Best Mathematical and Logic Puzzles (Dover Recreational Math).

The AMS collection is a great deal for anyone who likes math.

Amazon review

Goodreads review

Comments

★★★★☆ The Chinese classic novel with WOMEN!

The Story of the Stone Cao Xueqin There are four widely-recognized classic Chinese novels. Seriously, do a web search for "classic Chinese novels" and you will find dozens of pages referring to "The Four Classic Novels of Chinese Literature". (Wikipedia lists six on its Classic Chinese Novels page" -- these include the usual four, plus two others.) The phrase "Four classic Chinese novels" also appears frequently in commentary on Chinese literature. The four are Romance of the Three Kingdoms The Water Margin Journey to the West The Story of the Stone, or The Dream of the Red Chamber Red Chamber is distinctly different from the first three. It is the only one that feels (to me) like a modern novel. For instance, there are WOMEN! And they are not mere objects or cardboard cut-outs, but real, complex characters who carry the plot. Cao intended Red Chamber to be a memorial to the women he knew in his youth. And there is a love story! The protagonist, ...

★★★★☆ HE HAS TEETH. SHE HAS A GUN. THEY ARE THE LAW.

Wild Country Anne Bishop Anne Bishop likes cops. I can say with certainty that she likes them as characters in her books. Wild Country is the seventh novel in the Others and the World of the Others series. Each of these seven novels features policemen prominently. Monty (Crispin James Montgomery) is one of the most important characters of the five Meg Corbyn novels. Lake Silence has Wayne Grimshaw. Furthermore, I suspect that Bishop likes cops in real life, too. They are not universally good guys in her books -- there are bad cops. But those who are main characters are presented sympathetically. Wild Country , however, is the first novel of Others that features a cop as protagonist. That would be Jana Paniccia. Jana fought hard to become a cop. The police academy in Hubbney had little use for women, and her classmates didn't think a woman could be a good cop. She emerged successful, and also with a giant chip ...

★★★★★ Finding a home

The Blue Sword Robin McKinley When I was growing up my father's job kept my family moving. Mom and Dad eventually settled down, but just when they did I became an itinerant academic, moving to study and work at various research institutions. I was a 27 year old grad student at Stanford when I first read The Blue Sword and the longest I had ever lived in one place was six years. (Understand, I am not complaining -- I was and am a Happy Nomad.) There's a peculiar type of homesickness experienced by rootless people. One usually thinks of homesickness as being away from and missing a very specific place -- the place one calls home. But I had no place to call home. And yet I sometimes felt homesick -- I felt the lack of a home -- all the more because there was no home where I longed to be. In the first few chapters of The Blue Sword I immediately recognized this feeling of rootless homesickness in Angharad (Harry) Crewe, the hero of the book. As the book begins Harry ...

★★★★★ A brilliant mess

Long Live Evil Sarah Rees Brennan The publisher's blurb for Sarah Rees Brennan 's Long Live Evil makes it sound like a funny book about a real-world character who slips into a book and finds herself the villain. And it IS that! There were many laugh-out-loud moments, such as this one Books often described kisses as ‘searing’ which made Rae think of salmon, but characters seemed to enjoy the seared-salmon kisses. or this “You saw this horse born,” Marius reminded ... “I told you his bloodline could find their way anywhere. You named him.” “That was a joke,” ... Marius didn’t see what was humorous. He’d thought it was a nice name. ... “So this is my noble steed, Google Maps?” Rae, our heroine/villainess, is a fantasy book lover, who knows all the plot tropes, not to mention the movies and songs. Plugged into a fantasy novel (à la Inkworld or Thursday Next -- both are referenced in the Acknowledgments) Rae reacts like the thoroughly modern young wo...

★★★☆☆ What a difference a few inches make...

Fed Mira Grant **Spoilers for Feed follow ** (Also spoilers for Deadline and Blackout , but I will protect those in spoiler tags. Fed is an alternative ending for Feed . It is available free from Orbit books as a PDF download. At 53 pages it's either a long short story or a very short novella. When I reviewed Feed , I wrote, "The book ends well". Feed ended with Shaun Mason putting a bullet in the brain of the love of his life, his sister Georgia Mason, because she had become a zombie. (That's the big spoiler for Feed I promised above.) I thought this was a splendid ending. Tragic, yes, Gruesome, yes, but Feed is, after all, a zombie novel. I added the remark, "While I say, 'The book ends well,' I'm pretty sure that many readers are going to be unhappy with the ending." That was certainly true. For instance, one Amazon reviewer, following in the long tradition of people inventing ar...

★★★☆☆ Monsters of the forest and the lab

Boneyard Seanan McGuire Boneyard is the third novel in the Deadlands Series , based on the RPG of the same name. This is not, in my experience, a promising origin for a novel, but in my quest to read all of Seanan McGuire 's fiction, I read it. I have not read and do not intend to read any other books in the series (or to play the game). Since this is book 3, I have undoubtedly missed out on some world-building. Here's what I gather from Boneyard : the series takes place in an alt history world in which the Mormons managed to establish a technological empire in Deseret (what we call Utah) based in part on the uses of a substance called ghost rock. Most of that, as it turns out, is not very important to this installment. Despite its ominous sound, the word "boneyard" refers to a commonplace thing. When a traveling carnival stops in a town, in addition to the rides and shows they set up a support camp where the carnies can live, get fed, etc. This camp is called th...

★★★★★ Extraordinarily lucid exposition of an extraordinarily difficult subject

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering Steven H Strogatz My review of the first edition of Nonlinear Dynamics and Chaos follows. Everything I say there applies to the second edition as well. Aside from minor corrections, the second edition differs from the first mainly in the addition of new exercises. Strogatz writes in the Preface In the twenty years since this book first appeared, the ideas and techniques of nonlinear dynamics and chaos have found application in such exciting new fields as systems biology, evolutionary game theory, and sociophysics. To give you a taste of these recent developments, I’ve added about twenty substantial new exercises that I hope will entice you to learn more. Review of the First edition Nonlinear Dynamics is one of the most difficult areas of Applied Mathematics, but you would hardly guess that from reading Steven H. Strogatz . You can read No...

★★★★☆ Ramona Qimby meets a dragon

The Tears of a Dragon Intisar Khanani OK, that title is a lie. Intisar Khanani 's The Tears of a Dragon is not really about Beverly Cleary 's Ramona Quimby meeting a dragon. Or is it? The Tears of a Dragon is a novella in Khanani 's Dauntless Path series. It immediately follows The Bone Knife . Both stories concern a family in rural Menaiya. The father trains horses and has three daughters: Niya, Rae, and Bean. Bean, the putative Ramona of this family, is the youngest. In The Bone Knife the sisters helped a visiting Elf, Genno Stonmane, and he gave each of them a gift. Bean's gift was a small stone horse, which she wears on a thong around her neck. A troop of soldiers visits their village, and the gossip is that they have captured a baby dragon, whom they plan to use as bait to kill the mother. Bean is outraged and drags her sisters into a ill-planned raid to rescue the baby dragon. It's a good little story. S...

★★★★★ Faery Cosmology

Be the Serpent Seanan McGuire Regarding spoilers: I wrote most of this review before reading Be the Serpent , based on what I thought was coming. (Thus, it is not, strictly speaking, a review, but a preview, or perhaps a precognition 😀) I then read the book, and it turned out I needed to fix almost nothing. So, there are no spoilers here: nothing that could not be foreseen, except for one small one, which will be evident. Be the Serpent is one of the best October Daye novels to date. The best was The Winter Long . In The Winter Long Seanan McGuire did what I have come to see as the characteristic McGuire move: she rewrote the past. You may have thought you knew what was going on when you read Rosemary and Rue , but you did not. The Winter Long shows you that what actually happened in Rosemary and Rue was entirely different from the story Toby told in that book. The Winter Long completely reshaped...

★★★★☆ Tricky (in a good way!) Holocaust story

Hana's Suitcase: A True Story Karen Levine ** spoiler alert ** Hana's Suitcase: A True Story tells the story of Hana Brady, a Jewish girl who died, like so many, in the gas chambers of Auschwitz. It is she whose photo we see on the cover. Her parents were taken, then she and her brother George were taken to the Theresienstadt Ghetto , where they were held until 1944. Hana was put on the train to Auschwitz, where she died the day of her arrival. As the book reminds us repeatedly, a million and a half children were among the Jews killed. It is all too common a story. But Hana is special in one important way. Most of the millions who died vanished with barely a trace. Hana's story was told, mostly through the efforts of an extraordinary educator and researcher, Fumiko Ishioka. The problem with writing a children's book about the Holocaust is that, in the words of Aragorn, "it is sad, as are all the tales of Middle-earth". There are no happy stories of the Holoc...

Search This Blog