Square Date Surprises

April 15, 2009

Playing with numbers and dates can turn up all sorts of surprises. April 1, 2009, for example, written as 4012009, has 2003 as its square root. Hence, it's a square date.

That's just one tidbit that electrical engineer Aziz Inan of the University of Portland in Oregon discovered when he studied square dates. "I like to play with numbers and dates, and I'm always looking for math puzzles," Inan told USA Today. He regularly cooks up math quizzes for the historical newsletter, the Franklin Gazette.

A total of 68 perfect square dates occurred during the second millennium. Twelve of these perfect square dates occurred in the 16th century, and seven occurred during the 17th century. The dates Dec. 6, 1729, and June 4, 1764, were the only two perfect square dates in the 18th century (12061729 and 6041764 are the squares of 3473 and 2458, respectively). The dates April 25, 1844, and Jan. 30, 1881, were the only two perfect square dates during the 19th century. The last four of the 68 perfect square dates in the second millennium occurred during the 20th century: July 1, 1904; June 3, 1936; Mar. 17, 1961; and May 16, 1984.

The 21st century, surprisingly, will have 24 square dates, which is the most for any century until the year 10,000, Inan noted.

Mathematicians have long noted such numerical oddities. Augustus De Morgan (University College London), for example, once noted that 1849, the year of his 43rd birthday, had been the square of his age at that time (43 x 43 = 1849).

As for April Fools' Day, the next square date is April 1, 6016 (2004 x 2004 = 4016016).

Nonetheless, it's all a "nice little tidbit for April Fools' Day," said mathematician-magician Arthur Benjamin (Harvey Mudd College, in Claremont, Calif.), who knows what he's talking about. It's hard to surprise Benjamin, who is co-author of Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks.

Still, "if you look at numbers," Inan observed, "you start to see all sorts of patterns and that's always intriguing." One thing to keep in mind, however, is where you do your mathematics. In Europe and elsewhere, for instance, where dates are written differently, square dates wouldn't correspond to U.S. square dates.

Source: Beacon, Feb. 26, 2009; KOIN-TV (video); Oregonian, April 1, 2009; USA Today, April 1, 2009.