Maths Week England Puzzle Solution: How many people are in Ada’s class?

Ada’s class were told to get into equal teams to take part in a Maths Week competition. Trouble is, when they got into pairs, she was the only one without a partner. They tried teams of 3 people, but again she was the only one not in a team. They tried to get into teams of 4 people and this time Ada was still the odd one out! Finally, they got into teams of 5 and all was well – Ada was part of a team! How many people are there in Ada’s class?

And here’s a bonus solution – it’s a little more advanced using lowest common multiples and prime factors to give an infinite number of possible solutions!

Recorded for Maths Week England 2019 – more info here.

How to catch a Serial Killer with Hannah Fry

Hannah Fry (UCL) explains how police detectives use maths to help them catch a serial killer.

The second video featuring Hannah discussing the Maths of Data, first part here.

Find out how this method can be used to pinpoint the probable home of ‘Jack the Ripper’ courtesy of Tom Rocks Maths intern and Oxford University student Francesca Lovell-Read here.

Numberphile: Reynolds Number

The second of three videos I made with Numberphile on Fluid Mechanics. Reynolds Number is used to characterise a fluid flow and can lead to amazing results such as time-travelling fluids and the unsolved mystery of turbulence…

You can watch part one on the Navier-Stokes equations here.

Residencia de Estudiantes, Madrid

This week I had the honour of speaking at the Residencia de Estudiantes in Madrid, which has previously hosted Albert Einstein, Marie Curie, Salvador Dali and Igor Stravinsky amongst many, many others.

Ahead of the event I was asked a few questions by the organisers, and here are my answers.

Without revealing all your talk: could you give us an idea about how maths can help to be better at sports?

From calculating the perfect placement of a penalty kick in football to maximise your chance of scoring, to identifying the best location on Earth to try to break a world record, maths can be used to help to improve our performance in almost any sport. The difficultly lies in writing down the correct equations, but once we have them, maths has the answers.

Can you tell us any real example of this maths application?

My favourite example is one that will be featured in my talk: if attempting to break a world record in rowing, the best place to do so is on the equator. This may seem counter-intuitive at first, but as I will explain, by changing the location to the equator you can increase performance by up to 8%, which for an elite athlete is an incredible boost!

In your opinion: what makes maths so useful in different sports context?

Maths can be applied to anything. This is one of the main reasons that I love the subject and travel the world championing its versatility. Given a situation in any sport, you can always use equations to describe what is happening. This might be how a tennis ball moves through the air, or the aerodynamics of a swimmer gliding through the water. Once you have the equations, maths allows you to solve them for the optimal solution, which can then be translated into improved performance by changing your technique appropriately.

You also explain that the mathematical results in sports may vary, how? In which way? What should athletes take into account?

The ideas discussed in my talk are aimed at professional athletes who are already performing at a very high level and therefore need to resort to other approaches to improve performance beyond increased practice. For amateur athletes, whilst the same ideas will still be applicable, they are much more likely to benefit from practice!

What is your personal experience with sports? Have you ever used “math tricks” for optimise your scores?

The idea for the talk came from wanting to combine my two main passions: mathematics and sport. I play football regularly and as the designated penalty taker for my team have ample opportunity to try to hit the mathematically calculated perfect position for a shot. I also run marathons where my knowledge of the history (and mathematically predicted future) of the world record helps me to appreciate my accomplishments in the event.

How did you become a math communicator?

My first taste of maths communication came during my undergraduate degree at Oxford, where I joined the maths outreach group “Marcus’ Marvellous Mathemagicians”. The group was named after Marcus du Sautoy and performed interactive talks and workshops on his behalf in schools across the UK. The next opportunity came during my PhD when I spent two months working with the “Naked Scientists” team in Cambridge to produce a weekly science radio programme for the BBC. I enjoyed the placement so much that I agreed to join the team full-time upon completion of my PhD. After one year of working in radio production, I began to realise that my true calling was in video, and “Tom Rocks Maths” was born.

How are outreach, teaching and research connected in your professional life?

As someone who came from a state school background and worked extremely hard to get to Oxford, I have always had a passion for outreach and the drive to make university accessible to all. My maths communication work is an extension of this, allowing me to not only to visit schools in deprived areas to try to inspire them to consider higher education, but also to encourage the general public to engage more with the subject of maths and to no longer be afraid of numbers.

The teaching role fits perfectly with maths communication as both roles require the ability to be able to explain difficult concepts in ways that can be understood by a given audience. For a public lecture, the mathematical ability of the audience is perhaps less than that of a class of undergraduates, but the need for clear communication remains the same. In this way, I find that each role complements the other perfectly, with many of the topics that my students find difficult providing inspiration for future video ideas.

What do you enjoy most in your outreach talks?

There is nothing I enjoy more than being able to present to a live audience. Whilst I enjoy all aspects of my outreach work – YouTube, television, radio, writing – nothing beats the thrill of speaking to a room full of people who want to hear what you have to say. The small interactions with each individual member of the audience, whether through eye contact or answering a question, remain with me long after the event and act as one of my main motivations to continue with my work.

You are not the speaker one might expect when thinking about a maths communicator, what kind of reactions have you find in this sense? Do you have any anecdote regarding this?

There are two ways of looking at this: first, the notion of a stereotypical mathematician is outdated and from my experience not representative of a large part of the demographic; and second, I hope that by putting myself forward as a public face of mathematics I can help others who may be thinking that they can’t be a mathematician just because of the way that they look.

In terms of anecdotes, I think it best that I point you in the direction of the comments on my YouTube videos…

In particular, what are the reactions with “Equations stripped”? How did you come up with the idea of this series?

The “Equations Stripped” is possibly my favourite of all of the things that I do because it helps to tackle the idea that maths should be serious. The concept of the videos came from thinking about this opinion and trying to come up with what I thought was the best way to present the subject as anything but serious. The result is me talking about maths in my underwear!

My role with the “Naked Scientists” also played a part, as the name would often lead to listeners (or even guests) suggesting that we should all be naked when recording the show, and of course being a radio programme no-one could prove or disprove the theory! I always thought that we should have had more fun with this concept, and when “Tom Rocks Maths” was launched Naked Maths seemed like the way to go!

November 14, 2019 0

How are humans affecting bird populations in the UK?

Over the past 60 years since bird feeders first became commercially available, humans have been changing bird populations across the UK. The overall effect has generally been positive, with an increase in the prevalence of Wood Pigeons, and a shift in the migration pattern of Eurasian Blackcaps, but as with most changes, there is a word of warning… Live interview with BBC Radio Oxford.

November 12, 2019 0

How long is a lightning bolt?

A new record flash stretching all the way from Texas to Kansas was discovered recently in data from the GOES-16 spacecraft, though the record may soon be broken… Live interview with BBC Radio Oxford.

November 7, 2019 0

What is the impact of Christmas Jumpers on Climate Change?

Each year one quarter of the UK population buys a new Christmas jumper, despite a third of the UK already owning one, which made me think – what impact does this have on the environment?

Recorded for the Advanced Mathematics Support Programme (AMSP) as part of Maths Week England. More resources available here.

November 6, 2019 0

Funbers 28, 29 and 30

Fun facts about numbers that you didn’t realise you’ve secretly always wanted to know…

28 — Twenty-eight

28 has the infamy of being the second perfect number. This may sound like it came in second place in some kind of ‘best number competition’, but in fact a perfect number is one where all of the numbers that divide it, perfectly add up to give the number itself: 1 + 2 + 4 + 7 + 14 = 28. We first talked about perfect numbers back in Funbers 4.6692…, 5 and 6, which gives you a pretty big hint as to what the first perfect number might be…

Twenty-eight is also a triangular number. Building equilateral triangles using only dots gives rise to a sequence of numbers, each of which is called a triangular number. We start with a single dot, then we add a row of two dots below to make a total of 3, then we add a third row with three dots to give a total of 6, etc. etc. (see below for examples). For a triangle with seven rows the total number of dots will be 28. If you feeling brave, try to work out the general formula for the number of dots in a triangle with n rows.

Credit: Melchoir

So far I think we can say 28 is doing pretty well being both a perfect number and a triangular number, but it doesn’t stop there. Twenty-eight is also a magic number (yes, really). Magic numbers are a concept in nuclear physics which correspond to the total number of protons and neutrons required to completely fill a shell within an atom. There are seven magic numbers known so far: 2, 8, 20, 28, 50, 82, and 126 with at least another eight predicted by the theory.

29 — Twenty-nine

Here’s a fun challenge for you: using the numbers 1, 2, 3, 4 only once, along with the four basic operations of addition, subtraction, multiplication and division, can you make a total of 29? What about all positive numbers less than 29?

It turns out that 29 is in fact the smallest positive number that CANNOT be made using the method described above (it’s Funbers, you should have known there was a twist). In other claims to fame, it takes Saturn just over 29 years to orbit the sun, there are 29 states in India, and 29 Knuts make one Sickle in the currency of the wizarding world of Harry Potter. The real question is how many Sickles make a Galleon?

Credit: SunOfErat

30 — Thirty

As we enter the fourth decade of Funbers, let’s look back at some of the interesting numbers we’ve met so far… 1, 4, 9, 16 — what do they all have in common? Adding up the first four square numbers gives exactly 30: 1² + 2² + 3² + 4² = 30. This property makes it a square pyramidal number or a cannonball number. The latter name comes from the fact that a square pyramid can be built from exactly 30 cannonballs — instructions below if you want to try it out for yourself, though I recommend using something lighter and easier to obtain than medieval ammunition.

If you’re lucky enough to reach 30 years of marriage, you celebrate the Pearl Wedding Anniversary where, as the name might suggest, you traditionally receive a gift of pearls, although the ‘modern’ list published by the Chicago Public Library suggests a gift of diamond instead. Either way, sign me up. There are in fact suggested gifts for most wedding anniversaries — too many for me to include them all — so here’s a selection of some of my favourites. I’ll let you figure out which is the traditional gift and which is the ‘modern’ one…

1st — Cotton or a clock

3rd — Leather or glass

7th — Wool or a pen and pencil set

8th — Salt or linens

24th — Opal or musical instruments

85th — Wine or your birthstone

90th — Stone or engraved marble

Finally, let’s end with the magical and mysterious date of February 30th. It of course does not occur on the Gregorian calendar, where February contains 28 days in a typical year and 29 days during a leap year, and so is often used as a sarcastic date to refer to something that will never happen or will never be done. That is, unless you happened to be living in Sweden during the year 1712. Instead of changing from the old Julian calendar to the new Gregorian calendar by skipping forward 11 days as had been done in other countries, Sweden decided to do things differently. Their plan was to omit all of the leap days from 1700 to 1740, which would in theory have the same result, just over a longer time period.

There were 11 leap years during this timeframe (1700, 1704, …, 1740) and so this approach would have indeed worked, were it not for the Great Northern War. The war began in late 1700 and lasted for over 20 years, which unfortunately caused Sweden to ‘ forget’ to omit the leap days in 1704 and 1708, leaving them on neither the Julian or Gregorian calendars. To avoid confusion (and likely further forgetfulness) they restored the old Julian calendar in 1712 with the addition of the magical day of February 30th (visible in the image below). Which reminds me, I must let Taylor Swift know I can’t make our dinner date on February 30th…

Cover image credit: Lozikiki

November 5, 2019 1

Tom Rocks Maths S02 E11

A special edition of Tom Rocks Maths on Oxide Radio with music inspired by Tom’s recent visit to Slam Dunk Festival. We’ve also got Pokemon and drinking games, a mind-bending Einstein Puzzle, and news of Tom’s antics running around the streets of Oxford in his underwear… This is maths, but not as you know it.

October 29, 2019 0

Maths with a Striptease (Die Rheinpfalz)

Tom “rocks” maths on the internet – lecturer from Oxford arouses enthusiasm with crazy ideas…

The graduate mathematician Tom Crawford not only has rock music as a hobby, but he also looks like a rock star with his tattoos and piercings. However, some of his tattoos are related to mathematics. For example, the first 100 decimal places of Euler’s number wind around his arm and the number pi has been encrypted as an infinite series. On his Youtube channel “Tom Rocks Maths” he presents science in a fun way – the clothes sometimes fly during a striptease: “I want to show that maths is not always only downright serious, but fun.”

The math lecturer from Oxford came as part of the Heidelberg Laureate Forum (HLF) in the Electoral Palatinate. Since there is no Nobel Prize in mathematics, the winners (Latin: laureates) of comparable awards are invited to the HLF. The best math and computer scientists in the world meet here for a week with junior scientists and journalists. Crawford was on the ground as a publicist and presenter, and took the opportunity to speak to some of the awardees. For example, Martin Hairer, who received the Fields Medal for his seminal studies, had an appointment for an interview. In the end, they played Tetris for an hour and talked about “cool math”: “Such a relaxed and profound conversation is only possible at the Heidelberg Laureate Forum,” the Brit enthuses about the inspiring atmosphere at the HLF.

Tom Crawford was already “packed” in the elementary school of mathematics: “When we were learning multiplication, I did not want to stop working on difficult tasks until late in the evening – it did not feel like work at all.” Even later in high school, he always did math tasks first and gladly. “I was a good student in my eleven subjects, but math was the most fun.” The satisfying thing is, “in maths a result is right or wrong, there is no need to discuss it.”

After studying in Oxford, he went to Cambridge to write his PhD in fascinating fluid dynamics. “We wanted to model how fluids move and interact with the world. I was excited about the prospect of being able to analyse experiments as a mathematician.” From this, models of reality were developed: what path does a river take when it flows into the sea? The findings help to understand the pollution of the oceans and possibly stop it. During his PhD he worked for the BBC in the science programme “The Naked Scientists”: this meant that the scientists liberated their theories from the complicated “clothes” and reduced them to a comprehensible basis. In this way, a layman will discover “naked” facts – in the sense of comprehensible ones. The radio broadcasts were a great success.”But you also have to visualize maths,” so he started to make his own videos and took the concept of the “naked mathematician” literally. In some lectures, he reveals the equations “layer by layer” and in each stage falls a garment – until Tom remains only in his boxer shorts. And then his tattoos are also visible, on whose mathematical background he will give a lecture in Oxford soon – with many guests guaranteed!

With unusual ideas, the only 29-year-old mathematician arouses the desire and curiosity for his subject. His original internet activities have now been honoured with an innovation prize. Even when attending school in Schwetzingen Tom Crawford had unusual questions: “In the stomach of a blue whale 30 kilos of plastic have been found: How much would that be if a person swallows just as much in relation to their own body weight?” The students calculated that in the human stomach, six (empty) plastic shopping bags would be located. Or, “How many table tennis balls are needed to lift the sunken Titanic off the ground?” And which example impressed him most in mathematics? “It is terrific how Maxwell’s equations, which deal first with electricity and magnetism, follow the wave property of light with the help of mathematics alone. Math is just fantastic! ”

Birgit Schillinger

The original article published in the Die Rheinpfalz newspaper (in German) is available here.

October 24, 2019 0