Funbers 28, 29 and 30

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

28 — Twenty-eight

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Credit: Melchoir

29 — Twenty-nine

The_Making_of_Harry_Potter_29-05-2012_(7415385922)

Credit: SunOfErat

30 — Thirty

Square_pyramidal_number

Feb1712

Cover image credit: Lozikiki

Tom Rocks Maths S02 E10

Episode 10 of Tom Rocks Maths on Oxide Radio sees the conclusion of the million-dollar Millennium Problem series with the Hodge Conjecture, a mischievously difficult number puzzle, and the answer to the question on everyone’s lips: how many people have died watching the video of Justin Bieber’s Despacito? Plus, the usual great music from the Prodigy, the Hives and Weezer.

Image credit: Lou Stejskal

Funbers 25, 26 and 27

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

25 – TWENTY-FIVE

You probably know 25 as five squared, 5 x 5 = 25, but I bet you didn’t realise that it’s also the sum of the first five odd numbers: 1 + 3 + 5 + 7 + 9 = 25. It also crops up a lot in Pythagoras’ Theorem (yes, him again — see Funbers root 2) because it’s the smallest square that’s also the sum of another two square numbers: 25 = 3² + 4². Since Pythagoras’ Theorem says that a² + b² = c², we have the exact result with whole numbers (integers) for a = 3, b = 4 and c = 5. A solution such as this, where all of the numbers are integers, is called a Pythagorean Triple.

Looking beyond the maths, most videos are recorded at a frame rate of 25 per second as the PAL video standard – other options are available, but twenty-five does an excellent job of tricking the human brain into seeing a moving picture where in fact only a series of still images are being shown. Less than 25 and we might start to notice the ‘jumps’ between frames, and for more than 25 we’ll need a lot more data to record and store the footage.

equipment-731132_1920.jpg

Twenty-five is also the average percentage of DNA overlap between yourself and your grandparent, grand-child, aunt, uncle, nephew, half-sibling, double cousin (when siblings from one family have children with siblings from another), or identical twin cousin (if one of your parents is an identical twin and their twin has a child). Oh, and apparently a ‘pony’ is British slang for £25 – news to me…

26 – TWENTY-SIX

With twenty-five being a square number, and (spoiler alert) twenty-seven being a cube number, twenty-six is uniquely placed as the only whole number that’s exactly one greater than a square (5² + 1) and one less than a cube (3³ – 1). Talk about niche. And then there’s the fantastically named rhombicuboctahedron — a shape with 26 faces, made up of squares and triangles. Can you spot how many of each in the figure below?

Rhombicuboctahedron.gif

Twenty-six also gives the number of complete miles in a marathon (26 miles and 385 yards to be exact), the number of letters in the Latin alphabet, and the age at which males can no longer be drafted in the United States. The draft has been used five times throughout history: the American Revolution, the American Civil War, World War 1, World War 2 and the Cold War (including Korea and Vietnam). Let’s hope it never has to be used again.

27 – TWENTY-SEVEN

Now this one’s a real doozy: 27% of our universe is made up of “dark matter” – matter that has mass but is also completely invisible and doesn’t interact with itself or regular matter. The rest of the universe consists of 5% regular matter (the stuff we know about), and the other 68% is completely unknown. Something, something, dark energy…

Sticking with scary thoughts, in Stephen King’s novel ‘It’ (great film by the way) the creature returns to the town of Derry every 27 years, which also happens to be exactly the right amount of time for a new-born baby to join the 27 Club — a term used to refer to popular musicians who have died at the age of 27. Current members include Jimi Hendrix, Kurt Cobain and Amy Winehouse amongst many, many more. We also have 27 books in the New Testament and 27 bones in the human hand.

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Ending with some maths — what else — twenty-seven is the only positive whole number that is exactly three times the sum of its digits: 2 + 7 = 9 and 9 x 3 = 27. It’s also a perfect cube, 33 = 3 x 3 x 3 = 27, and it’s equal to the sum of the digits from two to seven, 2 + 3 + 4 + 5 + 6 + 7 = 27. But, leaving the best until last, if you label the decimal places of the number pi, starting from 0, then the 27th and 28th digits read 27. It may seem like magic but it’s actually one of a few ‘self-locating strings’ in the number. The others being 6, 13598, 43611, 24643510, and no doubt many more yet to be discovered. That can be your homework…

π = 3.141592653589793238462643383279…

 

Image credit: Jonathan Kis-Lev

Funbers 22, 23 and 24

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

22 – TWENTY-TWO

Coming in hot, 22 happens to be one of my favourite numbers – if you divide it by 7 you get about 3.142, which is a handy way of getting close to pi without having to remember all the digits! Then of course there’s Joseph Heller’s famous novel Catch-22. In the book, Catch-22 is the Air Force policy which says that bomber pilots can only stop flying planes if they are declared insane. But like the name suggests, there’s a catch. Catch-22 says that asking for a mental evaluation to get declared insane is proof that you aren’t in fact insane. So technically, there’s a way to get out of flying more bombing runs… but if you try it, you get sent right back out in the next plane!

Catch22-plane

Twenty-two also pops up in the kitchen. Normally, if you are slicing a pizza using 6 cuts, you’d do it neatly and end up with 12 even slices – much like the numbers on a clock face. But if you were a lazy pizza chef and just sliced randomly, you could end up cutting slices in half and ending up with more pieces. And it turns out, the most pieces you can end up with after 6 cuts is, you guessed it, 22!

On a darker note, 22 was also the lucky number of the Haitian voodoo dictator Francois “Papa Doc” Duvalier. Papa Doc started studying voodoo folklore to spread rumours that he had supernatural powers, which let him rule through fear. But eventually, he started believing the rumours himself. He would only go outside his palace on the 22nd of the month, because he thought he was guarded by voodoo spirits on that lucky day. He even claimed to have killed JFK, whose assassination was on the 22nd of November 1963, supposedly by stabbing a voodoo doll of him 2222 times that morning…

1963haiti_duvalier

23 – TWENTY-THREE

For 23 we’re going back to maths, and specifically prime numbers. A prime number remember, is one that can only be divided by itself and one without giving any remainder. Twenty-three has the unique property of being the smallest prime number which is not a ‘twin prime’ – that is a prime number which does not have another one within two spaces of it on the number-line. For example, 3, 5 and 7 are all close friends, while 11 and 13 go together. 17 is next to 19, but the nearest prime number to 23 is either four places below at 19, or six places above at 29, making it the smallest prime number to not have the ‘twin’ property.

Twenty-three is also big for birthdays. Not because the age of 23 is particularly special (although being the age mentioned in my favourite song – Blink 182’s ‘what’s my age again?’ – I do have a soft spot for it), but because of its appearance in the ‘Birthday Paradox’. The complete explanation is a little too long for Funbers, but in short it says that if you choose 23 people at random and put them in a room together, there is a greater than 50% chance that 2 of them share the same birthday. If that sounds too crazy to believe, check out a full explanation here from one of my students who applied it to the 23-man England squad for the 2018 Football World Cup. Now to enjoy some classic pop punk: “Nobody likes you when you’re 23…”

24 – TWENTY-FOUR

Who remembers Avogadro’s constant for the number of atoms contained in one mole of a substance from high school Chemistry? No, me neither. But, a great way to approximate it is using 24 factorial – or 24! in mathematical notation. The factorial function (or exclamation mark) tells you to multiply all of the numbers less than 24 together. So, 24! is equal to 24 x 23 x 22 x 21 x 20 x 19 x … x 2 x 1, also known as an incredibly large number. It’s about 3% larger than Avogadro’s constant, but certainly easier than remembering 6.02214076 x 1023.

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Twenty-four also represents the number of carats in pure gold, the number of letters in the Greek alphabet (ancient and modern) and the number of points on a backgammon board. Mathematically, 24 is the smallest number with exactly 8 numbers that divide it – can you name them? And, it’s equal to exactly 4 factorial: 4! = 4 x 3 x 2 x 1 = 24. Last but not least, where would we be without the 24 hour day – or to be precise 24 hours plus or minus a few milliseconds to be completely exact…

Day length
Yesterday 24 hours -0.46 ms
Today 24 hours -0.39 ms
Tomorrow 24 hours -0.35 ms
Shortest 2019 24 hours -0.95 ms
Longest 2019 24 hours +1.67 ms
Last Year Average 24 hours +0.69 ms

 

Tom Rocks Maths: S02 E06

Another fun-filled hour of your favourite two things – maths and rock music – courtesy of Tom Rocks Maths on Oxide Radio. This week I’m joined by two of my students from Teddy Hall, Fran and Tom, who will be explaining their favourite mathematical topics, taking part in a bumper numbers quiz, and sharing some of their music tastes. Plus, the usual dose of Funbers, and excellent music from Panic at the Disco, Sum 41 and Muse.

With thanks to Alice Taylor for production assistance.

Countdown Youngest Winner: Kai Laddiman

Kai Laddiman was the youngest ever ‘Octochamp’ on the gameshow Countdown when he was 11 years old, and also happens to be one of my students at the University of Oxford. I spoke to him about his experience 10 years on and put him through his paces with some of the number rounds…

Tom Crawford, and Rockin’ Maths Matters

Esther Lafferty meets Dr Tom Crawford in the surprisingly large and leafy grounds of St Hugh’s College Oxford as the leaves begin to fall from the trees. It’s a far cry from the northern town of Warrington where he grew up.

Tom is a lecturer in maths at St Hugh’s, where, defying all ‘mathematics lecturer’ stereotypes with his football fanaticism, piercings, tattoos, and wannabe rock musician attitude, he makes maths understandable, relevant and fun.

‘It was always maths that kept me captivated,’ he explains, ‘ever since I was seven or eight. I remember clearly a moment in school where we’d been taught long multiplication and set a series of questions in the textbook: I did them all and then kept going right to the end of the book because I was enjoying it so much! It was a bit of a surprise to my teacher because I could be naughty in class during other subjects, messing around once I’d finished whatever task we’d been set, but I’ve loved numbers for as long as I can remember and I still find the same satisfaction in them now. There’s such a clarity with numbers – there’s a right or else it’s wrong. In English or History you can write an essay packed with opinion and interpretation and however fascinating it might be, there are lots of grey areas, whereas maths is very black and white. I like that.’

‘My parents both left school at sixteen for various reasons but they appreciated the value of education. My mum worked in a bank so she perhaps had an underlying interest in numbers but it wasn’t something I was aware of. I went to the local school and was lucky enough to be one of the clever children but it wasn’t until I got my GCSE results [10 A*s] that the idea of Oxford or Cambridge was suggested to me. I would never have thought to consider it otherwise.

‘I remember coming down for an interview in Oxford, at St John’s, arriving late on a Sunday night and the following morning I took a stroll around the college grounds  – I could feel the history and traditions in the old buildings and it was awesome. I really wanted to be part of everything it represented. I thought it would be so cool to study here so I was very excited when I was offered a place to read maths.

‘Studying in Oxford I found I was most interested in applied maths, the maths that underpins physics and engineering for example. ‘Pure’ maths can be very abstract whereas I prefer to be able to visualise the problems I am trying to solve and then when you work out the answer, there’s a sudden feeling when you just know it’s right.’

In his second year, Tom became interested in outreach work, volunteering to take the excitement of maths into secondary schools under the tutelage of Prof Marcus Du Sautoy OBE as one of Marcus’s Marvellous Mathematicians (or M3), a group who work to increase the public understanding of science.

‘I went to China one summer to teach sixth formers and it was great to have the freedom to talk about so many different topics. I spent another summer in an actuary’s office because I was told that was the way to make real money out of maths – it was a starkly different experience. I realised I was not at all cut out for a suit and a screen!’ Tom smiles. ‘I am a real people-person and get a real buzz from showing everyone and anyone that you can enjoy maths, and that it is interesting and relevant. I love the subject so much and I think numbers get a bad press for being dull and difficult and yet they underpin pretty much everything in the whole universe. They can explain almost everything and you’ll find maths in topics from the weather to the dinosaurs.

Take something like the circus for example – hula-hoops spinning and circles in the ring, and then the trapeze is all about trigonometry: the lengths and angles of the triangle. Those sequinned trapeze artists are working out the distances and directions they need to leap as they traverse between trapezes and its maths that stops them plummeting to the floor!’

Having spent four years in Oxford Tom then spent five years at Cambridge University looking at the flow of river water when it enters the sea, researching the fluid dynamics of air, ice and water, and conducting fieldwork in the Antarctic confined to a boat for six weeks taking various measurements in sub-zero temperatures. You’d never expect a mathematician to be storm-chasing force 11 gales in a furry-hooded parka, but to get the data needed to help to improve our predictions of climate change, that was what had to be done!

Tom also spent a year as part of a production group known as the Naked Scientists, a team of scientists, doctors and communicators whose passion is to help the general public to understand and engage with the worlds of science, technology and medicine. The skills he obtained allowed him to kick-start his own maths communication programme Tom Rocks Maths, where he brings his own enthusiasm and inspiring ideas to a new generation alongside his lectureship in maths at St Hugh’s.

A keen footballer (and a massive Manchester United fan) it’s no surprise Tom has turned his thoughts to football and as part of IF Oxford, the science and ideas festival taking over Oxford city centre in October, Tom is presenting a free interactive talk (recommend for age twelve and over) on Maths versus Sport – covering how do you take the perfect penalty kick? What is the limit of human endurance – can we predict the fastest marathon time that will ever be achieved? And over a 2km race in a rowing eight, does the rotation of the earth really make a difference? Expect to be surprised by the answers.

Esther Lafferty, OX Magazine

The original article can be found here.

Arithmophobia – the fear of maths

New research shows that most parents can’t help their kids with maths homework because they have a fear of numbers. Here’s me being asked about the problem (and setting the presenters a farm animal themed maths puzzle) along with Martin Upton of the Open University on BBC Radio Scotland…

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