Funbers 31, 32 and 33

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

31 – Thirty-one

Hands up if you like ice cream? And your favourite brand? I’m not sure I could pick a favourite myself, but Baskin-Robbins is certainly up there. They have a total of 31 flavours of ice cream which means the name of their shops in Japan literally translates as ’31 Ice Cream’. In theory a great idea, but what if they discover a magical new thirty-second flavour…

Aside from frozen goods, thirty-one is also the number of teams in the National Hockey League, with 24 coming from the US and 7 from their Northern neighbours Canada. Each season, the teams battle it out to win the Stanley Cup — the oldest trophy to be awarded in professional sport in North America, and also the one with the infamously large base (see below). Originally, key members of the winning team were engraved on the base, which means its grown a fair few inches over the past 126 years. However, these days the oldest band is removed and replaced with a new one to prevent the trophy from getting any bigger. Less fun no doubt, but perhaps sensible given its already considerable size…

Andy_Saucier_with_Stanley_Cup_2017-06-11_16188_(2)

Credit: Michael Miller

Thirty-one is also a Mersenne Prime — the third such one in fact. A Mersenne Prime is a prime number that can be expressed as exactly one less than a power of two: 2^n — 1 for some positive whole number n. To get 31, we take n=5: 2⁵ = 2 x 2 x 2 x 2 x 2 = 32 minus 1 gives 31. A perhaps surprisingly large (and possibly infinite) amount of prime numbers take this form, with the current largest known prime number also being a Mersenne Prime: 2⁸²⁵⁸⁹⁹³³–1 = a number with 24,862,048 digits, aka too many for me to write out here!

32 — Thirty-two

Sticking with maths, thirty-two has the very nice property that it can be written as 1 to the power 1 plus 2 to the power 2 plus three to the power three, or in its neatest form: 1¹ + 2² + 3³ = 32. Here’s a challenge for you: can you work out the next largest number that follows the same pattern?

32 can also be written as 2⁴ + 4² = 32 which makes it a Leyland Number. Any number that can be written using two other numbers x and y, in the pattern x to the power y plus y to the power x, is classified as a Leyland Number. Here, we take x = 2 and y = 4 to get: 2⁴ = 2 x 2 x 2 x 2 = 16, plus 4² = 4 x 4 = 16, giving a total of 16 + 16 = 32. Other Leyland Numbers include: 8, 17, 54, 57 and 100 — I’ll leave it to you to figure out the specific values of x and y needed to satisfy the formula x^y + y^x = Leyland Number for each of the cases above.

Outside of the mathematical world, thirty-two is the number of completed piano sonatas by Ludwig van Beethoven; the number of black (or white) squares, and total number of pieces on a chessboard; the number of teeth generally found in an adult human; and the number of described physical characteristics of the historical Buddha, according to the text of the Pāli Canon in the Theravada Buddhist tradition. It’s a pretty long list, but I think it is best enjoyed in its entirety, so here you go:

  1.  Level feet
  2.  Thousand-spoked wheel sign on feet
  3.  Long, slender fingers
  4.  Pliant hands and feet
  5.  Toes and fingers finely webbed
  6.  Full-sized heels
  7.  Arched insteps
  8.  Thighs like a royal stag
  9.  Hands reaching below the knees
  10.  Well-retracted male organ
  11.  Height and stretch of arms equal
  12.  Every hair-root dark coloured
  13.  Body hair graceful and curly
  14.  Golden-hued body
  15.  Ten-foot aura around him
  16.  Soft, smooth skin
  17.  Soles, palms, shoulders, and crown of head well-rounded
  18.  Area below armpits well-filled
  19.  Lion-shaped body
  20.  Body erect and upright
  21.  Full, round shoulders
  22.  Forty teeth
  23.  Teeth white, even, and close
  24.  Four canine teeth pure white
  25.  Jaw like a lion
  26.  Saliva that improves the taste of all food
  27.  Tongue long and broad
  28.  Voice deep and resonant
  29.  Eyes deep blue
  30.  Eyelashes like a royal bull
  31.  White ūrṇā curl that emits light between eyebrows
  32.  Fleshy protuberance on the crown of the head

33 — Thirty-three

Let’s start with the bad. Thirty-three is one of the symbols of the Ku Klux Klan, with K being the 11th letter of the alphabet and 3 x 11 or 3 K’s giving 33. It is also believed to be the age of Jesus when he was crucified by the Romans.

On a more positive note, 33 is the longest winning streak ever recorded in NBA history, which was achieved by the Los Angeles Lakers in the 1971–72 season. We also find 33 vertebrae in a normal human spine when the bones that form the coccyx (the tail-like part at the bottom) are counted individually.

Now I don’t say this often — mainly because I think I’m supposed to be impartial when writing these — but this next fun fact is one of my all-time favourites. Long playing records, or LPs as they are more commonly known, are referred to as 33’s in the record industry, because they rotate 33 and a third times per minute when playing on a gramophone. So, next time you see a record player you know what to do…

Common-vinyl-record-dimensions-for-vinyl-to-cd-transfer-1024x407

Funbers 3

The number 3 is big in the worlds of literature and religion where most things like to come in threes. We have three musketeers, three Buddhist treasures and three Norse Norns… naturally.

 

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford 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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