### FRIDAY THE THIRTEENTH

The number 13 is usually associated with being an unlucky number. Buildings with more than thirteen stories typically will omit the number 13 from the floor numbering. This is immediately noticeable in the elevator, where there is no button for 13. You can certainly think of other examples where the number 13 is associated with bad luck. This fear of the number 13 is often referred to as triskaidekaphobia. Among the more famous people in history who suffered from triskaidekaphobia are Franklin D. Roosevelt, Herbert Hoover, and Napoleon Bonaparte.

You will likely recall that when the 13th of a month turns up on a Friday, there are some folks who believe that there could be particularly bad luck on that day. This may derive from the belief that there were thirteen people present at the Last Supper, which resulted in Jesus's crucifixion on a Friday. Do you think that the 13th falls on a Friday with equal regularity as it does on the other days of the week? You may be astonished that, lo and behold, the 13th comes up more frequently on Friday than on any other day of the week. This fact was first published by the American mathematician Bancroft H. Brown (1894–1974) in American Mathematical Monthly. He stated that the Gregorian calendar follows a pattern of leap years, repeating every 400 years. The number of days in one four-year cycle is 3 · 365 + 366. So, in 400, years there are 100(3 · 365 + 366) – 3 = 146,097 days. Note that the century year, unless divisible by 400, is not a leap year; hence the deduction of 3. This total number of days is exactly divisible by 7. Since there are 4,800 months in this 400-year cycle, the date of the 13th comes up 4,800 times. Interestingly enough, the 13th comes up on a Friday more often than on any other day of the week. The following chart summarizes the frequency of the 13th appearing on the various days of the week. Here we have a conundrum: the day that occurs most frequently is considered bad luck!

There are some people who were not consciously affected by the number 13 but have had much of their lives involving this rather-famous number. For example, the famous German opera composer Richard Wagner was born in 1813 (and the sum of the digits of this year is 13), and his name consists of 13 letters. Wagner was first motivated toward his life's work at a performance of Carl Maria von Weber's opera Der Freischütz on October 13, 1822. Wagner composed 13 operas. One of his operas, Tannhäuser, was completed on April 13, 1845, and was first performed in Paris during his exile from Germany on March 13, 1861. He spent 13 years in exile for political reasons. Wagner's last day in the city of Bayreuth, Germany, where he had built his famous opera house, was September 13, 1882. His father-in-law, the Hungarian composer Franz Liszt (1811–1886), saw Wagner for the last time on January 13, 1883. Wagner died on February 13, 1883, which just happens to be the 13th year of the unification of Germany. Curiosities such as these bring another dimension of entertainment to numbers.