# Perfect Christmas Tree Math

Here's a fun little post for the holidays!  It's not going to teach any new math concepts, though it is a neat demonstration of an out of the ordinary use for mathematics.  It describes mathematically how to decorate the perfectly proportioned Christmas tree.  I can't honestly say that I have tried it myself, though I don't doubt that it might be useful!

A department store in the United Kingdom by the name of Debenhams issued a challenge to the University of Sheffield math students to devise a mathematical algorithm to determine the optimum number of ornaments, tinsel, and lights in relation to the size of the tree, as well as the perfect size of the star for the top of the tree.  Members of the University's SUMS Math group were able to come up with a set of equations that described precisely what the challenge required:

 Courtesy of http://www.shef.ac.uk/polopoly_fs/1.227830!/image/formulaslarge.jpg
The students say that the calculation took about two hours to design, though to actually compute the equations is as simple as entering numbers into a calculator.  The stated purpose of the formula is to help holiday shoppers to be smarter when purchasing decorations for their tree, as with this knowledge they will be able to buy the precise number of baubels and lights rather than have a box of extras leftover once the tree is done, or else not have enough and so have to go and fight through the mall crowds to get more.  It also means that people can find the right size angel or star for their tree, rather than guessing and then potentially being way off when they actually get home.  They say that the formulas are versatile enough to apply to large trees suitable for the Royal Family, right down to smaller trees that are more common.  You can check out the original news release here.

It's probably a stretch to think that this set of equations will make it into widespread use, as decorating for the holidays is way more about spending time with friends and family and having good times, rather than looking for mathematical precision in a Christmas tradition.  However, it's a fun exercise to show young math students that demonstrates yet another useful and unexpected use of math in everyday life.

Happy Holidays to all of my followers, and all the best in the New Year!