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## UGH-ly Use of Mathematics

January 1...that infamous day when New Year Resolutions are made, a tradition traced back to the Babylonians. Supposedly 50% of all Americans make New Year Resolutions....with sincere intentions. The same data shows that 20% of the resolutions made...are broken by the end of the first week of January.

As a strange tie-in and perhaps an odd use of mathematics, let's turn to an expression for computing what is known as the "most depressing day of the year." This expression** is: [1/8W+(D-d) 3/8*TQ]/[M*NA], where

• W is weather
• D is one's debt
• d is the money due on January's pay day
• T is the time since Christmas
• Q is the period since the failure to quit a bad habit (i.e. first breaking a New Year's Resolution)
• M stands for one's general motivational levels
• NA is the need to take action and do something about it
Publicized by the BBC in January 2005, this equation was concocted by Cliff Arnalls, a part-time tutor at Cardiff University in Wales...great credentials! Based on Arnalls calculations, the "most depressing day of the year" in 2005 was January 24th. Also, it was later revealed that Arnalls developed the formula to help travel agents sell mid-winter tropical getaways.

Have some fun with your students trying to figure out how to calculate the "most depressing day of the year" for 2006. How does one quantify things such as the weather, one's motivational level, and the need to take action? Also, what is the format of the numerical output of the expression, i.e. does one get a single number (ordinal number 1-365) or two numbers (month and day)? Make sure you discuss the implications of this week's Humor as well.

And while you are at it, why not ask your students to create algebraic expressions for the "happiest day of the year." Share it with the local press. Who knows, they may receive fame equal to that of Mr. Arnalls.

**It is important to note that the reporting of the algebraic expression is not consistent...sometimes it is reported as 1/8W+(D-d) 3/8*TQ M*NA, which seems odd because an operation sign is apparently missing between the variables Q and M.