# Dear Dirichlet Christmas special

Moonlighting agony uncle Professor Dirichlet answers your personal problems this Christmastime. Want the Prof’s help? Send your problems to deardirichlet@chalkdustmagazine.com.

### Dear Dirichlet,

My flatmates and I put up our square-shaped artificial Christmas tree last week and decorated it beautifully. However, when I get home from work, I find it on its side on the floor. I think my flatmates are pushing it over but it doesn’t matter how much I shout at them, they insist it’s not their fault. Do you know why this is happening?

— Tinselitus, Glasgow

Dirichlet says:

Check the determinant of your quadratic tree. You should find that the solutions to your tree are of the form

$$holly + \mathrm{i} v,$$

where $\mathrm{i} = \sqrt{-1}$ and $holly, v \in \mathbb{R}$. You are probably having problems because $v \neq 0$, i.e. your tree has no real roots.

### Dear Dirichlet,

I’m cooking our annual Christmas dinner for my friends this year and I’m worried that it’s going to be a disaster. A few years ago there were only six of us, which I could handle, but since then our friends have starting bringing their friends, and this year they’re all bringing plus-ones. I’m terrified that the numbers are multiplying out of control. Am I stuffed?

— R. Cratchet, London

Dirichlet says:

Don’t worry, Bob. Multiplying numbers of guests is a scary proposition: maybe you would be happier with just a small addition of guests instead? Try logarithms to turn multiplication problems into simple addition. In fact, I highly recommend for this time of year the yule log.

### Dear Dirichlet,

My dog looked a little under the weather a week ago and a friend of mine suggested that I should find something to perk him up. I was looking for something natural, and the herbal remedies shop on the high street sold me this clearish liquid which I was supposed to add a few drops of to his water bowl. Anyway, yesterday I woke up and found that he has two bumps on the top of his head. And by this morning, they’d grown to a couple of inches in height! I think he’s growing antlers?!

— Ted Maltin, Twin Cities, Minnesota

Dirichlet says:
This is fixable but you need to act now. First, stop using modular arithmetic: remove all the clocks and pianos from your house. Then get rid of any congruences in your dog’s life: make sure all his biscuits are different shapes and toss away any copies of Despicable Me. Finally, take a few days off from work: if you stop commuting, the effect should break down.

It should clear up in a few days but you should have been more careful. Looks like you bought some dodgy Chinese Reindeer Serum.

### Dear Dirichlet,

My wife tells me that my gift presentation skills often leave a bit to be desired. You seem like a man who has Christmas all wrapped up; do you have any Christmas present packaging tips?

— Chris Moss, Troy

Dirichlet says:

Let $X$ be the present. First, prove the existence of a compact covering space over $X$ embedded in a suitable subspace of $\mathbb{R}^n$. The rest is trivial and left as an exercise for the reader.

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