Today is Pi Day, the date that is closest to the value of the mathematical constant Pi (3.14159…). Mathematicians are excited about this year. 2025 is a perfect square: it is 45 squared. The number 45 itself is a special number. It is one of the “triangular numbers.” That means that, starting at one, a sequence of natural numbers sum to it. In this case, 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45. Because of these two facts, there is a cornucopia of curious mathematical expressions that are equivalent to the number 2025, such as this one: 13 + 23 + 33 + 43 + 53 + 63 + 73 +83 + 93 = 2025.

The last year that had these mathematical properties was the year 1296. Such a year will not come again until the year 3025. Enjoy it while you can, math nerds!

The branch of mathematics that explores triangular numbers is Number Theory. One book on the Krueger Library retention list which discusses triangular numbers is:

Rademacher, Hans. Topics in Analytic Number Theory. Berlin: Springer-Verlag, 1973. 

Recap: In 2022, twenty-four Minnesota libraries joined together in a commitment to retain over a half-million print books which are scarcely-held in Minnesota. It is called the Minnesota Shared Print Collection. This is one of the stories from the Winona State share of the collection.

(Credit for pointing out to me these mathematical details goes to Paul Weiner, the retired Chair of the Math Department at St. Mary’s University, and to his number theory chums.)