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## December 12, 2012

### 12/12/12 and the Myriad of Number Patterns in Dates

Photo by Mohi Kumar

Today as you are slogging through the tasks marked on your calendar, you might notice the date: 12/12/12. This will be the last date with the same number for day, month and last two digits of the year until New Year’s Day, 2101 (01/01/01)–89 years from now.

Many are celebrating the date with weddings (the truly hard core are start their ceremonies at 12:00 pm, presumably so that they’d be mid-vow at at 12:12), concerts–such as this benefit for victims of Superstorm Sandy–even mass meditations. The Astronomical Society of the Pacific, based in San Francisco, has actually declared 12/12/12 “Anti-Doomsday Day,” the antidote to purported Mayan prognostications that the world will end on 12/21/12. Belgian monks have released the holy grail of beers–Westvleteren 12–for public sale today.

But even if you’re not doing something grand to commemorate the last such date in most of our lifetimes, you might find that a closer look at the date itself is intriguing from a mathematical point of view. As Aziz Inan, a professor of electrical engineering at the University of Portland whose hobby includes looking at number patterns in dates, describes (PDF) among other things:

• 12 = 3 x 4 (notice the numbers here are the consecutive counting numbers)
• 12 = 3 x 4, and 3 + 4 = 7; the date 12/12/12 happens to be the 347th day of 2012

On 12/12/12, there will be 12 days until Christmas. Twelve is also significant to society, the Astronomical Society of the Pacific reminds us. Aside from 12 inches in a foot, there are “contemporary calendars (12 months in the year), chronology (12 hours of day and night), traditional zodiac (12 astrological signs), Greek mythology (12 Olympic gods and goddesses), holiday folklore (12 days of Christmas), Shakespeare (Twelfth Night), and of course in our culinary world (dozen eggs, case of wine)…More importantly, in astronomy, Mars is 12 light minutes from the Sun, the average temperature of the Earth is 12 degrees Celsius, and Jupiter takes 12 years to orbit the Sun.”

The first 12 years of the next century will see 12 more dates with repeating numbers–01/01/01, 02/02/02, etc.–but other dates with numerical patterns are in our future. Here are a few categories:

Cheating but repeating: Every decade of this century will experience at least one date where all the numbers are the same–2/2/22, 3/3/33. 4/4/44, etc. The next decade will also have  2/22/22. Future dates out of reach for us–take 2/22/2222–may be truer representations of repetitive numbers in dates–imagine having that birthday!

Number palindromes: Palindromes–a number that reads the same forwards and backwards–are more common than repeats. This year hosted 2-10-2012. If you write dates in the “Gregorian little-endian” style of day/month/year, then 2012 had two: 21/02/2012 (in February) and 2/10/2012 (in October). The next palindrome date will be next year on 3/10/2013 (in March or October, depending on how you read the date). One-hundred and nine years from today, 12/12/2121 will also be a palindrome date. Inan has identified 75 palindrome dates this century–you can see the first 30 on a list he compiled. Of course, if you only use the last two digits of the year, then this past February (in the month/day/year way of noting dates)  was full of them:  2/10/12, 2/11/12, 2/13/12, etc.

Perfect squares: Some dates, like March 3, 2009 (3/3/09) are unique in that their numbers form perfect squares and their roots (as in 3 x 3 = 9). Other such dates are 4/4/16, 5/5/25, etc. But in some cases, if you take out the punctuation separating the dates, the resulting number is a perfect square. Take April 1, 2009, written as 4/01/2009 or 4012009–the number is a perfect square, with a root of 2003 (2003 x 2003 = 4012009). Other dates, when written the same way are reverse perfect squares, as Inan coined, when written from right to left. One such date December 21, 2010–when reversed it is 01022121, which happens to be the perfect square of 1011. Only two more such dates will occur this century.

Still other categories abound. Dates that are the product of three consecutive prime numbers (PDF), such as July 26, 2011, are an example; the date, when written as 7262011, equals 191 x 193 x 197. One date that is a simple sequence of consecutive numbers–1/23/45–will pop up every century. And my personal favorite, pi date (3/14/15), is only about two years away!

What other mathematical patterns in dates tickle your fancy?

Posted By: Math,puzzles |