*Today’s guest post comes from Madison Hodson, an instructor at AcerPlacer who recently earned her BS in mathematics from Weber State University. Congratulations, Maddy! We are all very proud of you!*

Merry Christmas everybody, it’s Maddy from AcerPlacer! Today I would like to talk about the Mathematics of Christmas. This article is based on the book *The Indisputable Existence of Santa Claus* by Dr. Hannah Fry and Dr. Thomas Evans. Today I’ll be talking about a few of the most important aspects of Christmas such as wrapping the Christmas tree in garland, buying presents, and – of course – the existence of Santa Claus.

If you are thinking of adorning your tree in garland, but are unsure how much garland you’ll need to buy – have no fear, there is a formula for you to use that will provide you with the exact length of garland needed for your Christmas tree! Let’s first make a little sense of the equation before I present it to you. If *h* represents the height of your Christmas tree, *r* is the radius of the base, and *n* is the number of loops around the tree you want your garland to make, knowing all of those numbers can help you plug them into this equation and presto – you’ll get out the perfect length for your garland!

Happy wrapping!

Moving on to the presents, it’s likely that most of us want to maximize our gift giving and receiving during a gift exchange. Please note, this doesn’t always mean giving and receiving to most expensive gifts you can find! What we will use in this next equation is the value of the gift you will give, the value of the gift you will receive, and those warm fuzzy feelings you get while giving the gift. These variables will provide us with a much simpler equation than the one we just looked at:

*Total Utility = Value of the gift received – value of gift offered + beneft of offering gift*

Now it might be hard to quantify the benefit of offering a gift (those fuzzy feelings) so to make it simpler just assume that the benefit is equal to have to half of the gift’s value. Now our equation looks like this:

There may be a few challenges in attaining maximized gift giving and receiving, such as determining the value of the gift before you actually receive it (which would ruin all surprises), but hey – the possibility is out there!

Last but definitely not least, let’s talk about the existence of Santa Claus. In the book the authors make two claims:

- An existing Santa exists.
- An existing Santa does not exist.

We know that one of these statements is true, but statement 2 seems to contradict itself so let’s take a closer look at it. Can an existing Santa not exist? By definition, something that exists “has reality, being, or lives,” so then an existing Santa must be alive and must be real. This means the second claim is false, leaving the first claim to be true!

There you have it, folks – Santa is real, maximized gift giving is attainable, and your Christmas tree will be Instagram worthy with its perfectly wrapped garland.

Until next Christmas, may your math be merry and bright!