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Dear Dirichlet Valentine’s Day special

Agony uncle Professor Dirichlet answers your personal problems this Valentine’s Day.


Moonlighting agony uncle Professor Dirichlet answers your personal problems this Valentine’s Day. Want the Prof’s help? Send your problems to

Need a Dear Dirichlet Valentine’s Day card? We’ve got you covered.

Dear Dirichlet,

I feel like my fiancé and I are continually going round in circles. Despite living together, the distance from our workplaces means that we’re shattered by the time we get home and, as a product, we get cross. I don’t want to set rigid rules for our careers, but we keep saying that we’re going to find jobs in a new town, and six months later we’re still in the same position. Have you fixed this problem for anybody?

— Uptown girl, White bread world

Dirichlet faceDirichlet says:

The two of you need to take a moment to stop pulling against each other and just torque. You can’t expect a happy equilibrium all the time, but as long as you don’t force it, you should be able to change your angrier momentum and become a happy couple.

Dear Dirichlet,

But, soft! What light through yonder window breaks? It is the east, and Juliet is the sun. But, like the sun, I only see her on high, shining from her balcony, many braccia above my head. How I long to be able to run up and see her, but all I can do is bite my thumb and cry out from the ground. It’s also often a bit windy and this makes communication difficult. Can you help?

— R. Montague, Verona

Dirichlet faceDirichlet says:

Fear not, fortune’s fool. Under the envious moon, simply apply the skew matrix $$\begin{pmatrix}1 & 0 & \tan\alpha \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{pmatrix}$$to young Juliet’s house, and you will find that the imposing front bows down before you. For ease of calculation, I recommend $\alpha = \pi/4$, but if you prefer a shallower ascent, $\alpha=\pi/3$ or $5\pi/12$ will smell as sweet.

Dear Dirichlet,

I’ve been dating my girlfriend for three weeks now and I am in blissful freefall. Everything started so fast but it just feels so right. I’m sure she’s the one but how can I know that the relationship will go the distance?

— Ken O’Mattock, somewhere along the M1

Dirichlet faceDirichlet says:
$$v^2 = u^2 + 2as.$$

Solve for $s$ where $v=0$, $u = \text{so fast}$ and $a = -9.8\,\mathrm{ms}^{-2}$. Many years ago I did this calculation, and the present Mrs Dirichlet and I have been together 20 years.

Dear Dirichlet,

I’m really up the creek this time. I’ve forgotten to buy my wife a Valentine’s Day present and now it’s too late to order off eBay. Surely she’ll know if I nip up to the petrol station. Many years ago I remember taking a couple of strips of paper, rotating one of the ends and then taping them into interlocking twisted loops. If I remember correctly, once I did that, I could cut along them in a special way to make some romantic interlocking hearts. Do you have the details so I can save my marriage?

— Non-orientable, Newport (South Wales)

Dirichlet faceDirichlet says:

Möbius strips should be band.


Heed Professor Dirichlet’s previous advice:

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Dear Dirichlet Christmas Special

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