There’s a lot of magic involved in Santa Claus’s annual journey around the world. Delivering presents to that many households can’t be done without it. But there’s also quite a bit of math. And I’m thrilled that Santa agreed to do this interview with us, revealing a few secrets of how math helps him in his work.

Can you explain what you do for a living?

Well, throughout the year, my main job is to oversee a large toy production facility at the North Pole. This includes supervising thousands of elves, who are responsible for toy manufacturing, as well as management of the reindeer stables, grounds work, sleigh maintenance and other smaller details.

But my main responsibility is only on one night of the year. On Christmas Eve, I pilot a large, flying sleigh, driven by eight reindeer and Rudolf, throughout the world to deliver presents to all good boys and girls. It’s a big night, and I usually take off the entire month of January to recover!

When do you use basic math in your job?

There’s a surprising amount of math involved in my work. These days, the naughty-and-nice list is in a database. A sophisticated set of formulas help me map out my once-a-year trip, which determines how the sleigh is packed. If Los Angeles gifts are on the top of the pack when I land in New York City — well, that’s a big problem.

I also need to manage my time, since I have so little of it that night. The different time zones help me stay a little ahead of the clock in most cases, but I sometimes have to do some on-the-spot figuring when weather becomes a problem.

But the real math is in the sleigh. Much like an airplane pilot, I must maintain a steady speed and take into account things like wind and visibility. The elves have helped equip the sleigh with state-of-the-art equipment, like gauges for altitude and speed. However, there have been some times when I’ve need to apply distance/speed/time ratios on the fly.

Do you use any technology to help with this math?

Absolutely. As I mentioned, we depend heavily on databases on the North Pole. These are housed in a large server, allowing us to manage our manufacturing quickly and easily. If a formula needs to be changed — for example, we need to greater ratio of purple bicycles to red bicycles — that alteration can be made in the database and applied throughout the facility. It streamlines the process considerably.

And I couldn’t fly to as many houses as I do today without my computerized dashboard in the sleigh. Each year, it’s calibrated to the specific weather conditions that are expected and even the current weight of the reindeer. Being able to customize these variables means making the most of those 20 hours that I’m in the sky.

How do you think math helps you do your job better?

I’m sure many people have said this: I couldn’t do my job without math. From the elves’ payroll to the naughty and nice list, every point of this whole operation hinges on how well we’ve done the math.

How comfortable with math do you feel?

I’d much rather talk to a child about what he or she wants for Christmas than sit down and solve a bunch of algebraic equations. But I’ve learned that in order to accomplish all that I do, I need to do some computing, too. I feel pretty comfortable with math, but it’s not my favorite thing in the world.

What kind of math did you take in high school?

School was a lot different way back then. You have to remember, I’ve been around for a long, long time! Heck, calculus wasn’t even invented yet, and forget about the calculator! But I did fine with the little bit of math I did take in school.

Did you have to learn new skills in order to do the math you use in your job?

When you’ve been in a job like mine for this long, you definitely have to pick up some new skills. The biggest changes have been technological. And once computers came on the scene, all of my operations had to be redesigned. I’ve even brought on some elves who are experienced with math modeling, so that we can stay ahead of any climate changes that will certainly affect our work. They’re developing up several models now with regards to the North Pole itself.

Thanks so much to Santa for taking time out of his incredibly busy schedule to answer a few questions. Happy holidays to everyone! In honor of the season, I’m going to take the rest of the week off. I’ll see you back on Monday, December 30, when we’ll kick off a really cool month designed to help you meet a special New Year’s resolution: brushing up on your basic math skills.

There’s a lot more to this time of year than the 12 days of Christmas, 3 wise men or 5 golden rings. Between digging out our credit cards and stringing hundreds of twinkly lights on the gutters, most of us have more numbers than sugar plums dancing in our heads.

And so, I bring you Christmas by the Numbers, a round up of interesting statistics about this huge holiday.

93: Percent of Americans (in 2008) who say they celebrate Christmas

81: Percent of Americans (in 2008) who identify with Christian faith

$427 million: Predicted sales of Christmas cards in 2012

4.1: Percent that holiday sales are expected to rise in 2012 over the previous year

12: Percent that online holiday sales are expected to rise

625,000: Predicted number of seasonal workers expected to be hired this holiday season.

25-30 million: Number of real Christmas trees sold in the U.S. each year

7: Average growing time (in years) of a six- to seven-foot tall Christmas tree

4,000: Number of Christmas tree recycling programs across the country

749.51: Dollars expected to be spent on gifts, decor and cards by the average holiday shopper this year

60: Percent of holiday shoppers expected to “self-gift”

1: Rank of gift cards in list of popular Christmas present requests

10: Percent chance of a white Christmas in my city (Baltimore, MD)

Any statistics that you’d like to see? Share your ideas in the comments section. Happy holidays!

elebrate Christmas, you’re heading into the home stretch!  As of this morning, there are nine days until the fat man comes down the chimney.  I hope you’re more ready than I am!  (My careful schedule has gone to pot, in some ways, derailed by a sick kid, aging dog and some unexpected work stuff.  But I’m getting back on track.)

If you’ve hung out with me here at Math for Grownups for a while, you know how much I love Vi Hart.  This chick is something else — a musician and a “recreational mathematician.”  (According to her site, she now calls herself a recreational mathemusician.)

In short, Vi is the daughter of a math professor and a wonderful musician in her own right.  She creates these really, really cool videos that explore the intricacies of mathematical concepts — from number theory to geometry.

Yeah, she’s a huge geek, but she’s one of those geeks who won’t make you feel dumb, and she’s funny.

This week, I came across her video, The Gauss Christmath Spectacular.  (Gauss was a 16th and 17th century mathematician who dabbled in a huge array of topics, from optics to statistics.)  There’s some stuff in here that will probably fly right over your head, but don’t let that discourage you.  Instead, grab a cup of eggnog, plop your favorite high school or college student next to you, and jot down the math that you do recognize.  You’ll probably surprise yourself.

Without further ado, Vi Hart’s take on the 12 Days of Christmas (my absolute favorite Christmas song when I was five years old — much to my parents’ dismay).

What did you recognize?  Show off in the comments section!

Ah, the cookie exchange!  What better way to multiply the variety of your holiday goodies.  (You can always give the date bars to your great aunt Marge.)

The problem with this annual event is the math required to make five or six dozen cookies from a recipe that yields three dozen.  That’s what I call “cookie exchange math.”

Never fear! You can handle this task without tossing your rolling pin through the kitchen window. Take a few deep breaths and think things through.

To double or triple a recipe is pretty simple — just multiply each ingredient measurement by the amount you want to increase the recipe by.  But it’s also pretty darned easy to get confused, especially if there are fractions involved.  (And there are always fractions involved.)

The trick is to look at each ingredient one at a time.  Don’t be a hero!  Use a pencil and paper if you need to.  (Better yet, if you alter a recipe often enough, jot down the changes in the margin of your cookbook.)  It’s also a good idea to collect all of your ingredients before you get started.  That’ll save you from having to borrow an egg from your neighbor after your oven is preheated.

Each year, I bring cow cookies to my neighborhood cookie exchange.  What are cow cookies, you ask?  Just what they sound like: sugar cookies cut into the shape of a cow.  The spots are made of melted chocolate.  (They’re Holsteins, of course.)  And around each of their little necks, I create little (icing) wreaths with red (icing) berries.

(Why do I make cow cookies?  It’s a long story.  But I’ve been these to holiday parties for more than 20 years now.  Kids love ’em.)

The problem is that my cow-shaped cookie cutter is larger than most other, eh-hem, more traditional Christmas cookie cutters.  So, while my recipe says it yields 36 to 48 cookies, I know I won’t get that many.

So each year, I triple the recipe.  That way I have enough for the cookie exchange (5 dozen), plus some to take to my mom’s house and give away to friends.

I can’t share the recipe here, because it’s copyrighted by Better Homes and Gardens (otherwise known as the Red Plaid Cookbook).  But we can look at the ingredient amounts.  My recipe requires the following measurements of various ingredients:  [pmath]1/3[/pmath] cup, 2 cups, 1 tsp and [pmath]3/4[/pmath] cups.

Since I’m tripling the recipe, I’ll need to multiply each of these amounts by 3. Then I can measure out the ingredients using the altered amounts.

The first three calculations are simple, but what about that last one?

The really easy way to get around this fraction is to fill a  one-fourth cup 9 times.  And honestly, if that’s how your brain works, go for it.

But if you want to, you could turn the fraction into a mixed number.  Here’s how:

Ta-da!  In only a few steps, I’ve done the simple math needed to alter this recipe.  Now, I just need to keep my fingers out of the bowl — so that I can actually bring enough cookies to the exchange.  (Honestly, I’d rather eat the dough than the baked and decorated cookies!)

What are your holiday recipe math tricks?  Can you think of other, more creative, ways to alter a recipe.  Share your thoughts in the comments section.