Funbers 7, 8 and 9
The fun facts about numbers that you didn’t realise you’ve secretly always wanted to know…
7 — SEVEN
‘I’ve sailed the seven seas, yarggg’ says a drunken pirate… There are of course more than seven seas — see how many you can name — but the point is that by seven we have reached what would have been considered a pretty large number in the past. Especially, amongst the less well-educated, such as pirates. We do, however, definitely have seven days of the week. The reason for this is thought to be due to the Babylonians, who measured time using the sun and the moon. The sun appears once each day and the moon once about every 29 days, making it pretty much once a month. The use of the seven-day week was probably because they wanted a smaller measurement between a day and a month and the best you can do with 29 is 4 lots of 7 (with one left over which I guess they just ignored).
The Romans are behind many of the names we use today for the days of the week, though the English ones have also been influenced by the Angles and Saxons, back when the Vikings were in charge. Monday is named after the moon, Sunday the Sun, Tuesday after Tiw — the Norse God of war, Wednesday after Woden — the chief Norse God, Thursday after Thor — the guy with the hammer and the God of thunder, Friday after Frigga — the goddess of marriage and finally Saturday after Saturn — the Roman God of time and harvest.
Seven is also the maximum number of circular objects that can be securely tied together in a bundle. It’s a lovely geometrical problem using the idea that exactly 6 circular objects will fit around a central circular object without leaving any gaps — you can try it out now with 7 coins on a table. If you try to add any more than 6 around the central one, gaps will appear, which would cause your bundle to fall apart.
8 — EIGHT
The number of legs on a spider, the number of tentacles on an octopus and now the number of planets in our solar system. There of course used to be nine until Pluto was demoted to ‘dwarf planet’ back in 2006. The reason? Astronomers found another dwarf planet called Eris that has a larger mass than Pluto despite being some three times further out, which ultimately led to the reclassification of what is and isn’t a planet.
Eight is a also big deal in Asia, like a really big deal. Its pronunciation in Chinese sounds the same as the word for prosperity and so its deemed to be a good luck charm. It also plays a big role in Chinese philosophy with the eight compass points — North, North East, East, South East, South, South West, West, and North West — each being assigned to one of eight moods and personalities, eight natural features and eight members of a family: mother, father and three children of each sex. No wonder they have an over-population problem…
9 — NINE
The last single digit number and one that we seem to like a lot as humans, maybe because of the 9 months we spend inside our mother’s womb before birth. It pops up in the animal kingdom too where cats are supposed to have 9 lives… unless you’re Spanish in which case they have 7.
You can also do a lot of fun mathematical tricks with the number nine. Take any number and multiply it by 9, then add up all of the digits, what do you get? Let’s try it out. 877 x 9 = 7893 and 7 + 8 + 9 + 3 = 27 and 2 + 7 = 9. This will happen every time. There are others too. Take any three-digit number, switch the first and last numbers around, and then subtract the smaller one from the bigger one. The middle digit of the number left is always a 9! That second one is a great way to trick your friends into thinking that you can read their mind…
The reason it works can be shown using algebra. It’s a word that has a bad reputation, but don’t let it put you off because it isn’t really that scary… (not until you get into n-dimensional spaces anyway). Let’s call your three-digit number a b c, where each letter represents the digit. First thing we do is switch the first and last ones around so now we have c b a. Before we can subtract the two numbers we have to make sure we keep track of which digit is in the tens column and which is in the hundreds column. So for our first number, we have 100a + 10b + c and for our second one we have 100c + 10b + a. Now subtracting one from the other we get: 100 (a-c) + (c-a) where the b vanishes. So importantly the tens column is empty and remembering that we subtracted the small number from the big number, we have that (a-c) is positive and (c-a) is negative. That means we have some number of hundreds, minus a single digit number. The smallest we can be left with is 91 and importantly there is no way to get anything other than a 9 in the tens column. Boom. There’s no such thing as mind-reading — sorry Derren — and we’ve just proved it using maths. Drops mic on floor…
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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