post

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!

10.

📐

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

9.

🏹

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

a.b = ab cos arrow

Continue reading

post

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!

post

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.

Continue reading

post

Football free-kicks… taken by Newton

This Saturday might be a normal day for many people, but football fans around the world are looking forward to it, as two of the best teams in the the world are playing in the final of the best club football competition, the Champions League, at the National Stadium of Wales in Cardiff.

Here at Chalkdust, we’re quite excited too, and so we decided to analyse the mathematics and physics behind one of the best goals ever scored… and go on to reproduce it mathematically!  You might find it provides an excellent topic of conversation in your preferred pub before the match or during half-time.

Continue reading

post

Taking the (mathematically) perfect picture at the Leaning Tower Of Pisa

Hundreds, perhaps thousands of tourists visit Pisa every day —mainly for its famous leaning tower. They rush from the train station, through the bridges and medieval alleys just to stand near the tower and take that picture they have dreamed of, posing in as many creative (and sometimes ridiculous!) ways as imaginable. The basic one is the Power Ranger, pretending to push the tower back to its vertical position, but there are many others: “I’m going to eat a tilted gelato”; or groups that pretend to push the tower as if it was Raising the Flag on Iwo Jima; or lovely couples, perhaps on their honeymoon, pushing the tower, each one on opposite sides (aww). Continue reading

post

The croissant equation

If you have a sweet tooth, then perhaps you enjoy just standing outside a fancy bakery and observing the many cakes and bakes from the shop, from their indulgent red velvet cupcakes, creamy sponges or decadent brownies. Cakes, cookies and cupcakes are complicated pieces of baking engineering which require sophisticated techniques to get the many flavours and textures into the single bite that you enjoy so much. Continue reading

post

Review of Elastic Numbers

I spend a lot of time solving maths puzzles. Many of my favourites appear in Chalkdust and on my website. But there is a problem with spending so much time doing puzzles: its not very easy for me to find new and interesting puzzles any more.

I was therefore pleased to hear that Daniel Griller—author of the Puzzle Critic blog, a great source of less well-known puzzles including this gem—was releasing a book of original puzzles. Elastic Numbers (Amazon UK, US) is this book, and boasts 108 puzzles. These puzzles are sorted into four sections by difficulty: bronze (easiest), silver, gold and diamond (hardest).

I highly recommend the bronze and silver puzzles to teachers, who will find a collection of well posed questions they can give to students to make them think about common school topics. However, these puzzles don’t offer much challenge to the seasoned puzzler, and although many are neat they feel a little unspectacular.

But the slight disappointment I was feeling about the book immediately disappeared when I flicked forwards to the gold and diamond puzzles. These puzzles will make you immediately reach for the nearest pen and paper and getting solving. With so many good puzzles in these sections, its hard to pick favourites, but the following puzzle stood out (so it’s perhaps not surprising that this puzzle is the source of the title of the book):

Elastic numbers

Source: Elastic Numbers by Daniel Griller (obviously)
A two-digit number $ab$ ($a$ and $b$ are the two digits of the number; the number is not $a$ multiplied by $b$) is called elastic if:

  1. Neither $a$ nor $b$ is zero.
  2. The numbers $a0b$, $a00b$, $a000b$, … made by putting any number of zeros between $a$ and $b$ are all multiples of the original two-digit number $ab$.

Find three elastic numbers, and explain why they are elastic. 

As any mathematician will be able to spot, Elastic Numbers is typeset in $\mathrm{\LaTeX}$. I greatly approve of this and the pretty equations it gives (we use $\mathrm\LaTeX$ for Chalkdust too), although this leaves the book looking more like a puzzle dictionary than a fun puzzle book that you might give straight to the kids. But to puzzlers like me, this doesn’t matter: the best thing about a puzzle is the new and exciting mathematical situation it gives you to investigate. And this book is packed full of mathematical excitement. And on that note, I’m off to work out where Evariste is standing…

Where is Evariste?

Source: Elastic Numbers by Daniel Griller (obviously)
Evariste is standing in a rectangular formation, in which everyone is lined up in rows and columns. There are 175 people in all the rows in front of Evariste and 400 in the rows behind him. There are 312 in the columns to his left and 264 in the columns to his right.

In which row and column is Evariste standing? 

post

In conversation with Marcus du Sautoy

For many people, Marcus du Sautoy might just be the most recognisable face in modern mathematics (although Carol Vorderman fans may disagree with this assertion!). He writes regularly for several national UK newspapers, is a frequent guest on the BBC and is about to release his fifth book. He has also taken mathematics to some more unconventional places, including the Glastonbury festival, the Royal Opera house and the Barbican. His academic work focuses on number theory and group theory, something that he says appeals to him due to its inherent structure, and because once you have the right idea “it kind of runs itself”. This love for big ideas and the story of mathematical discovery will be familiar to anyone who has ever seen him enthusiastically explain one of his favourite subjects, Euclid’s proof that there are infinitely many primes, on radio, television or in print.

The author of the article and Marcus du Sautoy standing, smiling, in du Sautoy's study

I feel sorry for all the toys with composite numbers on them.

However, despite his broad research background and his familiarity with, dare we say it, intimidating-sounding concepts such as ‘zeta functions of infinite-dimensional Lie algebras’, du Sautoy assures us that he is not the sort of person who “gets things really quickly”. This, he says, has helped him become effective at communicating mathematics—you must “get in the head of your audience” and understand why they aren’t comfortable with a concept, or “find the thing that they get, which you can use” to take them on the same journey that you have been through on your own road to understanding. In short, it is empathy.

Continue reading

post

The pipe singularity

Uproar and bewilderment had followed the plenary congress that had been held in the vast expanses of the imperial palace of Atzlan, the Aztec capital. Remotep, head of the royal laboratory, had made a great announcement. Following years of observations, studies and experiments, the renowned scientist had been able to forge a complete picture of the fundamental principles of life: this knowledge had already brought enormous advances to humanity but would soon completely revolutionise human existence.
Continue reading