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.

backgammon-789623_1920

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

 

How can you show geometrically that 3 < π < 4?

Approximating Pi was a favourite pastime of many ancient mathematicians, none more so than Archimedes. Using his polygon approximation method we can get whole number bounds of 3 and 4 for the universal constant, with only high-school level geometry.

This is the latest question in the I Love Mathematics series where I answer the questions sent in and voted for by YOU. To vote for the next question that you want answered next remember to ‘like’ my Facebook page here.

Funbers 2 Pi

Two times pi is such an important number in maths that it deserves its very own edition of Funbers… featuring angles, trigonometry and pie jokes.

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire here.

What is the Gamma Function?

The answer to the latest question sent in and voted for by YOU!

We’ve got probability distributions, complex analysis and of course Pi (because it appears everywhere)… I give you the Gamma Function.

To vote for the next question that you want answered remember to ‘like’ my Facebook page here.

Funbers 3, Pi and 4

The fun facts about numbers that you didn’t realise you’ve always wanted to know…

3 – THREE

Three’s a crowd… or is it? Imagine you’re writing a story, how many lead characters would you have? One means a hero, two means a love interest, and three comes next. This is why three is so popular throughout history – it’s the first number that allows for a team, without any romance. It’s also everywhere in religion: Christianity has the Holy Trinity, of the Father, the Son and the Holy Spirit; Islam has the three holy cities of Mecca, Medina and Jerusalem; Buddhism has the three Treasures of Buddha, Darhm and Sangha; Taoism has three deities called the Three Pure Ones; Brahma, Shiva and Vishnu are the three Hindu Gods and even going a little old school there are the three Norse Norns: Urd, Verdandi and Skuld who weave the tapestry of our fate with each thread representing the life of a single person… certainly something to ponder.

3.142… – PI

Everyone’s favourite mathematical food and quite possibly the most famous mathematical constant. Mathematical constants are numbers that aren’t part of the usual number line and aren’t fractions, but pop up everywhere in maths. I’ve already mentioned root 2, the Golden Ratio and e in earlier articles to name but a few. Physics loves a good constant too – the gravitational constant G is a classic, and hands up if you’ve heard of h-bar? (If you haven’t don’t worry physics isn’t as cool as maths). Going back to pi, it’s of course most famous for circles. Take any circle, measure its radius (the distance from the centre to the edge) and then the area of the circle is given by pi r2 and the distance around the edge of the circle (also known as the circumference) is 2 pi r. The fact that this works for any circle, ever, anywhere, that has ever previously existed or ever will exist, is what makes pi such a special number. The only explanation is that it’s part of the fabric of the universe. And it doesn’t stop with circles, pi pops up everywhere in physics too. Einstein’s equations for general relativity, check. Newton’s law of gravity, check. Maxwell’s equations of electromagnetism, check. I could go on, but I’d better get onto the next number… You get the point; pi is big news.

So big in fact, that you can watch a video I made for Pi Day (March 14th or 3-14 if you’re American) below.

4 – FOUR

Four is associated with symmetry, balance and stability. A table has four legs, lots of animals also have four legs (cows, sheep, pigs, lions, tigers, aardvarks, hippopotamuses…) and not forgetting even we have four limbs. There’s also the way we use four to divide everything up. There are four seasons in a year: winter, spring, summer and autumn, a compass has four points: North, East, South, West and there are four parts of the day: morning, afternoon, evening and night. The ancient Greeks went one step further and divided up everything in the world into one of the four elements: earth, fire, water and air. And their doctors believed that your body was filled with four liquids (which they called humors): blood, yellow bile, black bile and phlegm. If you were ill in ancient Greece, chances are your doctor would remove some of one of these liquids as an apparent cure… leeches anyone?

Then there’s the four horsemen of the apocalypse. I was a big fan of the Darksiders video game series growing up so I know all about these bad boys. They are mentioned in the Bible, though it’s difficult to know exactly what each one represents – sounds like most of the Bible to me… One is definitely death, that’s certain. The other popular choices are conquest, war (pretty similar no?) famine, pestilence and plague. Yes, that does make 6, but hey it’s the Bible, anything goes…

Oh, and I almost forgot, maths loves four too. There are four main operations: addition, subtraction, multiplication and division. It reminds me of the classic chat-up line: me plus you, subtract clothes, divide those legs and lets multiply… (crickets I know, but at least I tried).

You can find all of the funbers articles here and all of the episodes from the series with BBC Radio Cambridgeshire and BBC Radio Oxford here.

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