Funbers 0, 1 and 1.4142…

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

0 — ZERO

First up is a big fat round nothing. Can nothing be a number? Is zero even a number? A hot topic for debate amongst those that have time to debate such life-threateningly important issues… Zero is to numbers what white is to colours: its everything and nothing all at once. White is actually my favourite colour so I am absolutely definitely on team zero here — it’s a number. Zero is also incredibly important in maths precisely because it’s nothing. We mathematicians have these things we call ‘identities’ that must exist for maths to work. Even simple things like addition and multiplication don’t make sense without identities. For example, if you take any number and multiply it by 1 you get the same number you started with which means 1 is the identity for multiplication. For addition it’s the same, what do you add to a number so that you still get the same number? Spoiler alert its zero. If you add zero to a number, you get back the same number which makes zero the identity for addition. There are lots of other reasons why zero is important, but I think you get the idea — and it’s definitely a number.

1 — ONE

The most popular number in the world. Period (as our American friends would say). I already sort of cheated and told you above that it’s the identity for multiplication, but don’t worry it’s also a whole lot more besides. Along with zero (which is definitely a number), it’s the only number that is the square of itself, i.e. 1 x 1 = 1. It can also divide every number and it makes up half of binary code, aka the language of computers. And that’s not all. One is the atomic number of Hydrogen, this is the invisible gas that makes up about 75% of the universe, so probably pretty important… and without one there’d be no one-night stands, no one-liners and perhaps most importantly no one-hit wonders. What’s the biggest one-hit wonder of all time? I’ll give you a clue: it involves a silly dance that everyone knows from the 90’s…

1.4142… — ROOT 2

The square root of two or Pythagoras’ constant. I have no idea why this is named after Pythagoras (yes the same guy who loved triangles) because the Greek mathematician who discovered this number whilst studying at Pythagoras’ School was actually drowned for his sins. Yes, that is correct — some poor guy had rocks tied to his feet and was thrown off a cliff into the ocean because he did some clever maths. Maths just went badass people, don’t mess with Big P (Pythagoras to his friends). Back to the number root 2, it comes from Pythagoras’ triangle theorem, which you’ve hopefully heard of… It says that the lengths of the sides of a right-angled triangle are related by an equation a² + b² = c².

If you put a=1 and b=1, then c² = 2 and so c equals the square root of 2, or 1.4142… The dots here mean that the number goes on forever. It’s like pi, e and those other funky numbers that just keep going on and on and on. The reason the poor guy was drowned for discovering this number is because he showed that it cannot be written as a fraction. We can write 0.5 as 1/2 or 0.3333… (going on forever) as 1/3, but 1.4142… cannot be written in this way. For this reason it’s called an irrational number — that’s any number that you can’t write as a fraction. The usual suspects, pi and e are also irrational. As is the next number on my list — the Golden Ratio. But that will have to wait until next time.

Oh, and in case you didn’t work out the biggest ever one-hit wonder, here it is in all its glory…

Author

The Funbers series is written and presented by Dr Tom Crawford and is broadcast weekly on BBC radio. For more maths fun check out Tom’s website tomrocksmaths.com and follow him on Twitter, Facebook, Instagram and YouTube @tomrocksmaths.


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