There are dozens (maybe thousands) of websites that explain what triangular numbers, square numbers, etc. are. I'm searching for a printed book that includes this material, preferably at a level that would be appropriate for an elementary school-aged student (i.e., someone 11 or younger). It's not typically found in elementary school textbooks or other curricula, so this would probably need to be a "Cool Math"-type of extracurricular book. Does anybody know of such a source?
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$\begingroup$ Is it required to be in print and readily available for purchase? $\endgroup$– shooverJul 12, 2021 at 1:28
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$\begingroup$ @shoover Not necessarily, out-of-print books are fine. $\endgroup$– mweissJul 12, 2021 at 1:30
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$\begingroup$ A google books search for "figurate numbers" led me to Figurate Numbers by Michel Deza and Elena Deza, although this book is almost certainly too advanced for your needs. Also, most every older recreational math book before the 1950s or so has a section on figurate numbers, such as Hogben's Mathematics for the Million and Ball's Mathematical Recreations and Essays, and many such books can be found on university library shelves. $\endgroup$– Dave L RenfroJul 12, 2021 at 14:28
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$\begingroup$ I recommend The Number Devil, by Hans Enzensberger. Chapter 5 is about triangular numbers. But that's the only chapter on figurate numbers. $\endgroup$– Sue VanHattum ♦Jul 13, 2021 at 19:36
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There is a publication in the ERIC archive called Recreational Mathematics*, authored by William L. Schaaf, that is a bibliography of books and journal articles about recreational mathematics, organized by topic. A search in this document for "triangular numbers" yields quite a few results, for example, a page of books about "number curiosities":
A specific book that treats triangular numbers is Martin Gardner's Mathematical Carnival, which starts from Pascal's Triangle and shows the different sorts of numbers that can be extracted from it. As Gardner puts it, "the pattern is so simple that a 10-year-old can write it down."
I suggest a search through ERIC for some more recent references, or a search through the Internet Archive for some possibly older ones, may result in a list of suitable books. Some of the "out of print" books may have been revived in an affordable Dover printing.
*Not to be confused with the now-defunct Journal of Recreational Mathematics or the newer journal called Recreational Mathematics Magazine!
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1$\begingroup$ In addition to the places above, a useful reference to keep in mind for things like this is the 4-volume A Bibliography of Recreational Mathematics by William Leonard Schaaf Volume 1 (also here) and Volume 2 (also here) and Volume 3. I can't find a digital copy of Volume 4 (I have print copies of all volumes), but in it you'd want to look at Section 2.4: Figurate numbers on pp. 25-28. $\endgroup$ Jul 12, 2021 at 14:13
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1$\begingroup$ @DaveLRenfro The first page image above is from Schaaf. $\endgroup$– shooverJul 12, 2021 at 16:24
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2$\begingroup$ I realized this after I wrote my comment, when I clicked on your link. In fact, I initially thought you were referring to an issue of Journal of Recreational Mathematics, and only later realized this was the 3rd edition of Schaaf's bibliography. Note that my links are to the 4th edition (1970 for Volumes 1 and 2, 1973 for Volume 3; FYI, Volume 4 appeared in 1978). And while I'm here, I may as well mention David Singmaster's pages for those not familiar with them. $\endgroup$ Jul 12, 2021 at 16:49