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# Dear Dirichlet, Issue 04

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

### Dear Dirichlet,

This year has been a bit tough for us financially, and the only summer holiday we were able to afford was a week camping in the not-so-sunny East Midlands. My work colleagues, however, won’t stop talking about their blissful trips to the beaches of southern Europe. I don’t want to seem jealous but I wish they’d stop chatting about their suntans. How can I move the conversation on?

— Beyond the pale, Selly Oak

Dirichlet says:

I, too, sometimes crave the idyllic sands of southern Europe, but alas, circumstances require me to spend most of my days answering personal problems from my country house. I have, however, found a technique which gives the appearance of spending a few weeks in Marbs. On a sunny weekend, find a police constable. Ask to borrow her nightstick. Then simply divide the sunsinh with her cosh, and what do you have?…tanh, or as I like to call it, “fake tan”.

### Dear Dirichlet,

I am going to a conference in Toulouse in a few months’ time, and I have just discovered that my French crush, who grew up nearby, is also attending. I think it might be a prime opportunity for us to get to know each other better, if you catch my drift. But I don’t want to mess it up and waste my chance. You seem like a well-conferenced chap: how do I make the most of this opportunity?

— Je t’aime, J’habite dans le nord de l’Angleterre

Dirichlet says:

As I have often experienced on my visits to Paris, no one can resist the charm of the French. Let me share a technique that I have often, after some analysis, found to be useful. WLOG place yourself at $x_n$ and your crush at $x_m$. Then for any $\varepsilon>0$, ensure that there exists an $N$ such that $\forall n,m>N$, $|x_n-x_m| < \varepsilon$.
This will ensure that your elements will become arbitrarily close to each other as the sequence progresses. When your $\varepsilon$ is sufficiently small, seal the deal by whispering “voulez-vous Cauchy avec moi?”.

### Dear Dirichlet,

I have been trying to be self-sufficient this year with my vegetable patch down the allotments by the corn exchange, on Windy Lane (turn left at the bus stop), just by the freight railway, not far from the nuclear power plant. I say power plant: it’s more of a test site. I am hoping to make a nice soup from the pods that are growing down at the bottom of the garden, among the birds and the bees, at the end facing the sewer works, downwind from the (old) gas station, from where you can see the butterfly farm. I say butterfly farm; it’s more of a butterfly farn. For this recipe, I need the same weight (mass) of (single) cream and vegetables. However, to know how much (single) cream to buy, I need to know how many peas will grow. Help!

— Keen gardener, Allotments, Downwind from (old) gas station, nr. Butterfly Farn

Dirichlet says:Sounds like you’ve got an N-Pea problem! This will be hard to solve. Perhaps you can seek the advice of your local mathematician. He’s sitting in his favourite chair in his house on Orchard Close, backing onto the brook through the manor house that used to belong to Sir Alfred, overlooking the abandoned barn, not too far from the (second largest) ford. (I say ford: it’s more of a collapsed bridge.)

### Dear Dirichlet,

I was really worried about my options for my year abroad next year, so imagine how super-excited I was to hear that I am going to New York! I’ve got my visa sorted and have been trying to read up on life in America: driving on the wrong side of the road, never using the metric system, how to take a taxicab… But are there any special behavioural customs I should know about living downtown in the Big Apple?

— Worried about distance, Bicester South

Dirichlet says:

The Manhattan norm is given, for a vector $\boldsymbol{x}$, by

$\displaystyle \|\boldsymbol{x}\|_1 = \sum_{r=1}^n |x_r|$.

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