Top 10 emoji for use in mathematics

Maths loves symbols. Everyone loves emoji. It’s 2017 and time we brought the two together. To get you started, here are our top ten emoji for use in mathematics!



Don’t leave home without one: it’s the nifty 45° set square. What better reminder is there that
$$\sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}, \qquad \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}, \qquad \tan\left(\frac{\pi}{4}\right) = 1$$ 📐



Perfect for popping over a letter to make it a vector, it’s the bow and arrow:

a.b = ab cos arrow

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Making your own papercupter

Papercupter competition

Finding the best design for a papercupter is not easy as there are many designs, for instance, with longer or shorter flaps, curvier or straight, only a few flaps or as many as you can get from your paper cup. The number of different papercupters is infinite and so finding the one that spins the most or the one that stays in the air for the longest time is impossible.

There are some papercupter designs which clearly won’t work, for instance, one with flaps so small that it does not make the papercupter spin as it falls down, or one with so many flaps that they become thin strips of paper with no air resistance.

Last week we were able to play a papercupter competition (during the 2017 De Morgan Dinner) and more than 50 different designs competed against each other. The papercupters which made it to the final round had, in general, only a small number of long flaps.

Rosalba, winner of the 2017 Papercupter competition and her design for the best papercupter.

Try your own papercupter!

Different paper cups also have a different design for the best papercupter, but let us know in the comments below which was the best papercupter you could find! Also, send us your pictures and videos through Facebook, Twitter or by email!


What’s your least favourite number?

Mathematics doesn’t always involve working with numbers, but they crop up frequently enough for us to have developed some strong emotional responses to specific ones! Throughout the pages of Chalkdust Issue 5 we shared some of the numbers that we really dislike, and here we’ve collected them together. Do you have a least favourite number? Let us know at the bottom of this post.

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Prize crossnumber, Issue 05

Our original prize crossnumber is featured on pages 58 and 59 of Issue 05.


  • Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. As usual, no numbers begin with 0. Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.
  • One randomly selected correct answer will win a £100 Maths Gear goody bag. Three randomly selected runners up will win a Chalkdust t-shirt. The prizes have been provided by Maths Gear, a website that sells nerdy things worldwide, with free UK shipping. Find out more at
  • To enter, submit the sum of the across clues via this form by 22 July 2017. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 30 July 2017.

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On the cover: dragon curves

Take a long strip of paper. Fold it in half in the same direction a few times. Unfold it and look at the shape the edge of the paper makes. If you folded the paper $n$ times, then the edge will make an order $n$ dragon curve, so called because it faintly resembles a dragon. Each of the curves shown on the cover of issue 05 of Chalkdust, and in the header box above, is an order 10 dragon curve.

Left: Folding a strip of paper in half four times leads to an order four dragon curve (after rounding the corners). Right: A level 10 dragon curve resembling a dragon

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Dear Dirichlet, Issue 05

Dear Dirichlet

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to

Dear Dirichlet,

I personally have a very deep, long-held belief in free-market capitalism and the value of hard work, but I was recently shocked to discover when I switched subjects that most people in my new research area are staunch followers of Karl Marx! I’ve had many arguments with my new colleagues on this. I can feel my energy slowly draining with every passing debate. How do I resolve this?

— Feeling blue, Surreyv

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Page 3 model

Bread is a staple of many diets. From delicious garlic bread to crunchy pizza, it’s enjoyed throughout the world. But have you ever wondered what mathematics lies just beneath the crust?  Thankfully DR Jefferson, AA Lacey and PA Sadd at Heriot-Watt University have! No? Well, we’re going to tell you anyway.


Bread dough is initially a bubbly liquid, with bubbles connected to other bubbles in a ‘matrix’.  These bubbles will collapse, provided that both the temperature and temperature gradient are high enough. To start with, the bubbles at the surface (which is hotter than the interior) reach a temperature at which they are likely to fracture. At this point, the temperature gradient is also high, with plenty of cooler liquid dough nearby. However, when the temperature of the interior has increased sufficiently to allow the bubbles inside to burst, the temperature gradient is much lower, the matrix has set, there is less liquid dough nearby, and so less collapse can take place.


But that’s not all! We can refine the model by considering the movement of the ‘crust boundary’ (where bubbles collapse) as the dough rises, as well as the vaporisation of moisture inside the bubbles. Both of these allow for the transfer of heat and affect the thermodynamics of the whole process.


So in the future, please try to remember all the maths that worked hard to ensure the crustiness of your bread! And, on that note, we’re off to get pizza…


Jefferson DR, Lacey AA & Sadd PA 2007 Crust density in bread baking: Mathematical modelling and numerical solutions. Applied Mathematical Modelling 31 (2) 209–225.
Jefferson DR, Lacey AA & Sadd PA 2007 Understanding crust formation during baking. Journal of Food Engineering 75 (4) 515–521.