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Triskaidekaphobia! - Dr. Alfred Posamentier


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Believe it or not, there are people who fear the number 13. This is called Triskaidekaphobia (from Greek tris meaning "3" kai meaning "and", deka meaning "10" and phobia meaning "fear". Often this is a superstition and related to a specific fear of Friday the 13th, which is called paraskevidekatriaphobia or friggatriskaidekaphobia.

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 sometimes no button for 13. You might ask your students for other examples where the number 13 is associated with bad luck.

They ought to stumble on the notion that when the 13th of a month turns up on a Friday, then it is often considered a bad day. This may derive from the belief that there were thirteen people present at the Last Supper, which resulted in the crucifixion on a Friday. Yes, this month, January 13, 2012 falls on a Friday!

Ask your students if they think that the 13th comes up on a Friday with equal regularity as on the other days of the week. They will 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 B.H. Brown.* 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 x 65 + 366. So in 400 years there are 100(3 x 65 + 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 4800 months in this 400 year cycle, the 13th comes up 4800 times according to the following table. Interestingly enough, the 13th comes up on a Friday more often than on any other day of the week. Students might want to consider how this can be verified.

Day of the week          Number of 13s        Percent
Sunday                         687                            14.313
Monday                         685                            14.271
Tuesday                 685                            14.271
Wednesday                 687                            14.313
Thursday                 684                            14.250
Friday                         688                            14.333
Saturday                 684                            14.250

Perhaps one of the saddest examples of the bad luck of the number 13 is related to the launch of Apollo 13, which was launched on April 11, 1970 -  often written as 4-10-70. The sum 4+10+70=85, then 8+5=13. The launch was made from Pad 39 (which is 3x13) at 13:13 local time (i.e. 1:13 PM). It was struck by an explosion on April 13th!

Famous people have also been plagued by Triskaidekaphobia. These include: Franklin Delano Roosevelt, Herbert Hoover, Mark Twain, and Napoleon. One of the most famous and revolutionary music composers of all time, Richard Wagner was also closely tied with Triskaidekaphobia. It begins with Wagner's birth year, 1813, where the sum of the digits is 1+8+1+3=13. Wagner's famous festival opera house in Bayreuth, Germany was opened on August 13, 1876. He wrote 13 operas (or as they are usually referred to: music dramas). His opera, Tannhaser was completed on April 13, 1844. Its Paris version closed with some controversy on March 13, 1861 and reopened there on May 13, 1985. Wagner was banned from Germany for political reasons for 13 years. His last day in Bayreuth was September 13, 1882. Friend and father-in-law, the music composer Franz Liszt visited Wagner for the last time on January 13, 1883 in Venice, Italy. Wagner died on February 13, 1883, which was the 13th year of German unification. Oh, and by the way, Richard Wagner has thirteen letters in his name!

So you can see students can also have fun with numbers - a very important aspect of teaching mathematics: bring some lighthearted fun into the subject matter. #

* "Solution to Problem E36."American Mathematical Monthly, 1933, vol. 40, p. 607.


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