Skip to main content

★★★★★ 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

Popular posts from this blog

★★★★☆ Where Peter Pan and Tiger Lilly come from

Tigerlilja Erin Michelle Sky, Steven Brown In  J.M. Barrie 's  Peter Pan  Peter's great ally is Tiger Lily, who is introduced thus ...Tiger Lily, proudly erect, a princess in her own right. She is the most beautiful of dusky Dianas and the belle of the Piccaninnies, coquettish, cold and amorous by turns; there is not a brave who would not have the wayward thing to wife, but she staves off the altar with a hatchet. There's obviously a lot there that's problematic in the 21st century. So she gets a rewrite in this  Erin Michelle Sky  and  Steven Brown  prequel to  Tales of the Wendy . In addition, we get an origin story for Peter, something that to my knowledge  Barrie  never supplied. In fact, we start with Peter. Peter, it transpires, is descended from gods.  Sky  and  Brown  freely mix Norse and Greek gods here. In seeking to protect him from ancestral enemy Buri, Peter's mother accidentally curses him. You will forg...

★★★★☆ Lada the Impaleress

And I Darken Kiersten White Vlad Dracula , also known as Vlad the Impaler or Vlad III of Wallachia, was the Voivode (ruler) of Wallachia (a part of what is now Romania) between 1448 and 1477. He was a contemporary of  Mehmed the Conqueror , the sultan of the Ottoman Empire (which became Turkiye) who eventually conquered Constantinople (now Istanbul, as  They Might be Giants  reminds us), ending the Byzantine Empire. It was an exciting time in Asia Minor and Eastern Europe! A historical novel about Vlad and Mehmed thus seems like a great idea. What we have here, however, is  close  to, but not  exactly  that.  Kiersten White 's  Conqueror's Saga , of which  And I Darken  is the first book, is an alternative history version of that time and place. The "alternative" part comes in the shape of Ladislav (that's a feminine form of "Vlad"). In  And I Darken  the first child of Vlad II (who in the real world was the father of Vlad...

★★★★☆ A downtrodden hero and troll

Troll Bridge Terry Pratchett Cohen the Barbarian's father told him, he told him, "Son, when you can face down a troll in single combat, then you can do anything." Cohen wants to defeat a troll in single combat before he dies. But the task is beginning to look urgent. First, Cohen is no longer a young hero. As Cohen's horse tells him, "One day you're going to die. It might be today." That's the first problem. The second is that troll bridges are in short supply. As Cohen tells his horse, When did you last see a bridge with a troll under it? There were hundreds of 'em when I was a lad. Now there's more trolls in the cities than there are in the mountains. So, he's found an old stone bridge that still has a troll. The troll's name is Mica. Like Cohen, Mica is himself a relic of the old days. He is still proud to uphold the old trollish tradition of defending a bridge. What's more, he's chuffed at the prospect of being killed by a...

★★★☆☆ Vanja comes to terms with her history

Holy Terrors Margaret Owen Vanja Ros has a long history of disappointing people. She was the thirteenth child of Marthe Ros, and therefore, Marthe believed, ill-fated. She asked Death and Fortune to take her daughter. Death promised her, "Only one of you will go home." Death and Fortune gave their God Daughter Vanja a home. Vanja's mother never returned home from the forest. Marthe, now a ghost, is still furious about this. And so it went. Vanja went into service in a noble house and there she disappointed. Eventually she ended up as a thief. And then things got serious. A brilliant young prefect (police detective) came after her. She fell in love with him, and he with her, but she left him. She found her family and deceived them. She even became a goddess and failed at that. Now, to be clear, none of that is fair. It is, however, far too accurate a picture of how Vanja sees herself. When  Holy Terrors  begins, Vanja is estranged from Emeric, the prefect she loves, and sh...

★★★★★ 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...

★★★☆☆ The Handmaid’s Tale meets M*A*S*H.

Manacled senlinyu Some candid reactions as I read: 22%: "Make it stop. Please." 54%: "Once more unto the breach! Took a short break to read  Bookshops & Bonedust , which was released yesterday. To my surprise, I feel some eagerness to return to  Manacled  after the somewhat flaccid plot of  B&B ." 67%: "To be fair, a lot is done right. The characters are well drawn and the plot, as far as I've gotten, is very good, intricate and well-thought-out". 100% (last night): Thank God that's over. So, mixed reactions. This one is unusual for me. Usually I read fiction for enjoyment. If a book has a lot of stuff I like in it, that's a good book and gets all the stars. This is unlike most Goodreads reviewers. Judging from the reviews I read, most GR reviewers read books looking for things they don't like, then make a list and if there are lots of things they don't like, then no stars. (Or maybe that's just the way they write reviews.) ...

★★★★★ King of the Cats, Alice and Thomas, Fairies, bogeymen, and assorted entertainments

Patreon Year 5 Seanan McGuire I will begin by clarifying what I am reviewing here.  Seanan McGuire  has a Patreon Creator page. Patreon is a website where artists can share their work with subscribers. Subscribers pay a certain amount (usually monthly, but that varies from artist to artist), and in return get access to things ("rewards" in Patreon-speak) that the artist posts on Patreon. "Things" can mean images, videos, or (most relevantly in this case) eBooks. Typically there are multiple reward tiers -- the more you pay, the more you get.  McGuire  set up her Patreon page in June 2016 and has posted a story every month since then, which makes 64 now (September 30, 2021, when I am writing this), plus a few one-time extras. These "stories" can be pretty substantial literary works. For instance, the reward for July 2021 was an 80,000-word novel. The way Patreon works, if you subscribe to a tier, you typically get access to everything that was posted for th...

★★★☆☆ Veterinarian to magic creatures

The Magic and the Healing Nick O'Donohoe I believe I read  The Magic and the Healing  not long after it came out in 1994. I liked it and went on to read the rest of the  Crossroads trilogy . The whole thing had a clumsy feel, as if it was the work of an inexperienced author. Although that is not quite true, it is close.  Nick O'Donohoe  published a book in 1981,  April Snow , which was apparently entirely forgettable.  Crossroads  did better -- each of the three titles has a rating exceeding 4.0 on Goodreads. The books themselves, however, appear to be out of print, and neither of my local libraries has copies, so one has to guess their commercial success was limited. The protagonist is a veterinary student, BJ Vaughan, about to leave school because of some personal crises. She's your standard "gifted-but-unsuccessful" sympathetic hero. One of her profs, who believes she is a gifted vet, recruits her to come to the Crossroads, where she heals a un...

★★★★☆ Laziness spurs creativity

X-Men (Penguin Classics Marvel Collection) Stan Lee, Jack Kirby (Artist), Roy Thomas, Werner Roth, Don Heck, Neal Adams, Arnold Drake, Gary Friedrich, George Tuska, Ben Saunders (Editor), Rainbow Rowell (Foreword) The  X-Men  were born when  Stan Lee  and  Jack Kirby , Marvel's premiere creators of new superhero comics, noted that superhero teams such as the  Fantastic Four  were box-office, so why not start another one? Lee wrote Then once I figured out what powers they'd have ... how did they get their powers? And they were all separate people that weren't connected to each other, so I knew that would be a helluva job. And I took the cowardly way out, and I figured, hey, the easiest thing in the world: they were born that way. They were mutants. In a world in which nuclear weapons tests had in the recent past released lots of radioactivity in to the atmosphere, this appeared to make a lot of sense.  As a card-carrying geneticist, I have to tell ...

★★★☆☆ True lust conquers all

A Fate Inked in Blood Danielle L. Jensen ** spoiler alert **  Meet our first-person narrator Freya. She's a beautiful Norse woman who knows how to swing a sword. Her hair color is not at first mentioned, but we presume she's the blond pictured on the cover. Meet Bjorn. He's a big, extraordinarily handsome black-haired warrior. Much of his conversation consists of boasts of his sexual prowess, and women he's favored talk to other women about how great he is in bed. Freya and Bjorn meet cute (Freya literally throws a fish in his face), and of course they are immediately possessed by a desire to jump each other's bones. You know Freya feels this way because she's the narrator and you're in her head. You know the feeling is mutual because you're not an idiot -- besides, he eventually tells her. Before the end of the book they act on this desire, and we are presented with a detailed description of moist bits rubbing against other moist bits, along with the si...