Clifton Fadiman was host of Information Please!, the trivia radio show, from 1938 to 1948, which is why his name was naggingly familiar. I've only heard a few episodes, which is why it wasn't obvious. I'd have learned this sooner if I read the author's information on the cover.
I joked how remarkable it was there was a third story in the Fantasia Mathematica collection, but I'm of mixed feelings about the range of the mathematics-based stories. The book isn't explicitly science fiction, but might as well be, since the stories mostly use mathematical notions to carry out improbable mischief, and who can tell whether a character getting lost into the fourth dimension was published in The New Yorker or in Astounding?
Of 23 short stories -- including that bit of Plato where Socrates unconvincingly proves people are born knowing the Pythagorean theorem, but don't know it -- Möbius strips or Klein bottles figure in seven of them, including of course A J Deutsch's ``A Subway Named Moebius,'' in which the subway is not a Möbius anything. People getting lost in higher dimensions or warped space figures in five (some overlap with Möbius strip stories, like Deutsch's). Monkeys-at-typewriters figure in three, plus a note from Willy Ley in his role as interpreter/science popularizer. That topology stories predominate is understandable, since you can explain enough topology to whip up neat consequences easily and without blocks of mathematical symbols that earn Linotype operators hazard pay. You could do anything you like with Banach spaces of square-integrable functions and it'd be only a Macguffin; turning someone inside-out has consequences.
Still, explaining the construction of the Möbius strip in pretty much the same words seven times in the span of about ten stories is a bit much, even in William Hazlett Upson's very funny ``A. Botts and the Moebius Strip''. In that one a Möbius strip is used against an excessively focused World War II safety engineer. Perhaps most endearing is Harry Stephen Keeler's 1927 ``John Jones's Dollar,'' tracing the compound-interest descendants of a bank account of one dollar at three percent interest opened in 1921. It mentions that by 2921, the total wealth of the whole solar system -- including that of all eight planets, the other seven all colonized (the Moon was evicted from the solar system as a navigational hazard), and the projected value of all future solar radiations -- comes to just a touch under $6,310,000,000,000, which was owed to Mr Jones's descendant.
Trivia: The Möbius function is, for an integer, equal to zero if the integer has a repeated prime in its factorization; it is one if the number has an even number of unique factors; it is negative one if the number has an odd number of unique prime factors. Source: The Mathematical Experience, Philip J Davis, Reuben Hersch.
Currently Reading: Fantasia Mathematica, Clifton Fadiman, Editor.