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

★★★☆☆ Music with rocks in

Soul Music Terry Pratchett Soul Music  is the 16th novel in  Terry Pratchett 's  Discworld  series, and also the third novel in the  DEATH  subseries.  Discworld  is a long series -- 41 novels, not to mention the inevitable short stories. Any series so long is bound to be a little repetitive at times. Soul Music  seemed to me a kind of rehash of  Moving Pictures , on the one hand, and  Mort  on the other. Death (the  Discworld  character) is always slacking off. He gets tired of being Death and tries to take a vacation. The problem with Death taking a vacation is that he is what, these days, we call an essential worker. If Death takes time off, someone needs to fill in for him. In  Mort  that was Death's new apprentice Mort -- in  Soul Music  it is Susan, the daughter of Mort and Death's adopted daughter Ysabell. Susan is thus Death's granddaughter. The problem with putting a human in Death's job, ...

★★★★☆ 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...

★★★★★ 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...

★★☆☆☆ Misery, Canadian style

The New Oxford Book of Canadian Short Stories Margaret Atwood (Editor), Robert Weaver (Editor) I read  The New Oxford Book of Canadian Short Stories , (eds  Margaret Atwood ,  Robert Weaver ) because it is the textbook for a community college course I've registered for this winter called "Writing Short Stories". This is one of the worst short story collections I have ever read in my life. I noticed early on that it appeared to be the same story over and over again. A man and a woman are trapped in a desperately unhappy marriage. Maybe something happens, or maybe not. It is evident that for  Atwood  and  Weaver  plot is entirely optional. Some of the stories had one, and some did not. There were rare exceptions to the desperately unhappy marriage storyline, in which the characters were miserable for other reasons. You know that feeling of relief as you approach the end of a really bad book? I had that feeling 45 times in rapid succession as I worked my ...

★★★★☆ Two seriously messed-up people

Paladin's Grace T Kingfisher Stephen is a seriously messed-up guy. He is, or was, a paladin of the Saint of Steel. He bore within him a soul connection to his god, the Saint of Steel, who would use him to do good. Three years ago Stephen's god died, and since then he has been an empty man. He, and all the paladins of the late Saint of Steel, worry that if they lose control of their passions, they will be taken by "the tide" and run berserk, killing and destroying. This is not idle worry. It has happened, although not recently. Grace is a seriously messed-up woman, though she is arguably less messed up than Stephen. She grew up in an orphanage. She was, for all practical purposes, purchased by a master perfumer, who took advantage of her acute olfactory abilities without apparently feeling any obligation to treat her as a teacher should treat a student. He sold her to another perfumer who, in addition to taking advantage of her abilities, took advantage of her sexually...

★★★☆☆ Velveteen returns!

Velveteen vs Gainful Employment Seanan McGuire Velveteen vs Gainful Employment  is  Seanan McGuire 's October 2023 Patreon reward. Velveteen is the hero of a series of quite old stories by  Seanan McGuire , notionally published in three books: Velveteen vs The Junior Super Patriots , Velveteen vs The Multiverse , and Velveteen vs The Seasons . I say "notionally published" because most of these books are no longer available as books. You can still find the stories online however. If you click on the links for the books in the previous sentence, they will take you to my reviews of the books on Goodreads, and in each review there is a list of links to free online copies of the chapters. They are a lot of fun. Velveteen, AKA Velma Martinez, is a superhero whose superpower is the ability to animate dolls, stuffed animals, etc, and make them do her bidding. Used imaginatively this is a pretty awesome superpower that has allowed Velveteen to win most of her battles. The last sto...

★★★★☆ She was Joan of Arc. She was Athena. She was the Wendy.

The Wendy Erin Michelle Sky, Steven Brown I am a fan of  J.M. Barrie 's  Peter Pan . His dark view of childhood is refreshing, if you have met too many angelic children in literature. Seriously,  J.M. Barrie  uses the word "heartless" eight times to describe children. Off we skip like the most heartless things in the world, which is what children are, but so attractive; and we have an entirely selfish time, and then when we have need of special attention we nobly return for it, confident that we shall be rewarded instead of smacked. (Do your own research!  Here  is the Project Gutenberg full text of  Peter Pan . Do a text search for "heartless.") An even stronger selling point for  The Wendy  was the striking cover --    -- yeah, absolutely I want to read that! Don't judge a book by its cover, they say, but every now and then I do, and I am seldom misled. To be honest,  The Wendy  is not much like  Peter Pan . Wendy D...

★★★☆☆ More a themed collection of stories than a novel

When the Moon Hits Your Eye John Scalzi I found myself disappointed by  John Scalzi 's  When the Moon Hits Your Eye . That's mainly because I was hoping for a novel and didn't quite get one. In his acknowledgments,  Scalzi  summarizes the structure of  Moon ...a book about the moon turning to cheese, have each chapter represent a day in the lunar cycle, each chapter with mostly different characters in mostly different places in the Unites States, reacting to it in ways specific to them alone... Now,  Moon  does in fact have a coherent story with a beginning, a middle, and and end. The problem is that, told as it is, in short day-in-the-life stories with mostly different characters each, it doesn't have the stakes that make a novel really interesting. We don't spend enough time with any of these characters to get to know and care about them. That at least, was how I felt. Instead, it felt to me like a themed short story collection. Some of the stories w...

★★★★★ The second time I read Pride and Prejudice

Pride and Prejudice Jane Austen I remember exactly where I was the second time I read  Pride and Prejudice . I was in Uris Library at Cornell, the Undergraduate Library, affectionately known as the UGLY, sitting in the beautiful second-floor reading room. (The UGLY is not actually ugly at all.) I had read  P&P  once before, when I was in High School, and I loathed it. I probably picked it up again thinking that an author could not be as revered as  Jane Austen  is unless there was something there. Had I missed something? Had I ever! The first time I read  P&P , I thought every word was meant seriously. Thus, when  Austen  wrote, "It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife," I took that to be something  Austen  literally believed. The second time I heard the laugh, and I saw the key to reading  Austen : she is always laughing. Behind every sentence she ...