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.

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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?

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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

Ancient Greek Mathematicians

A new feature from Tom Rocks Maths – a weekly maths puzzle for you all to enjoy! Answers will be posted when the next puzzle is released so remember to check back and get your thinking hats on…

Below are portraits of three famous mathematicians from Ancient Greece. Your task is to give me the name of each of them along with one of their mathematical discoveries… Send your answers in on Facebook, Twitter, Instagram or via the contact form on my website. Good luck!

WARNING: answer below the picture so if you want to attempt the puzzle please scroll slowly to avoid revealing it!

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Answer:

(a). Archimedes – most famous for running naked down the street exclaiming “Eureka!” after discovering what is now called Archimedes Principle. It relates the buoyancy of an object to the weight of water and allows you to easily work out whether or not something will float.

(b). Plato – involved with many things, but mathematically best known for his interest in shapes. The 5 Platonic Solids bear his name and are also my favourite shapes. Plato thought that they were so beautiful the entire universe must be built out of them…

(c). Pythagoras – perhaps the most famous mathematician to have ever lived due the triangle theorem named after him that we are all taught at school. It tells us that the length of the diagonal side of a right-angled triangle c is related to the length of the other two sides a, b by a very neat relationship a2 + b2 = c2.

Funbers Root 2

Time for the next number in the Funbers series with BBC Radio Cambridgeshire and BBC Radio Oxford…

Also known as Pythagoras’ constant or 1.414… the square root of 2 is possibly the most ‘bad-ass’ of all numbers. Legend has it the man that discovered it was pushed overboard from a ship and drowned for his sins… Ouch.

 

Funbers 0, 1 and 1.4142…

The fun facts about numbers that you didn’t realise you’ve 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.

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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…

 

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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