## This is the story of rotations, reflections and enlargements and translations. It’s about an ingenious shape that lives in millions of households yet that few people have even heard of. And it’s the story of how some simple maths – GCSE transformations and a little geometry – led to a revolution in photography. This is the story of the Roof Pentaprism: a simple yet beautiful solid shape at the heart of every DSLR camera (that’s the posh ones!).

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__HOW CAN I MAKE MATHS FUN?__

## House Of Maths was recently interviewed on the radio about the new GCSE and “real life” maths problems. But while making maths relevant IS important, “keeping it real” doesn’t automatically make maths fun – especially if your teacher is more like Miss Trunchbull than Miss Honey. Instead, here are the six ACTUAL secrets of turning maths from boring to brilliant:

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**Isn’t maths great?** Everything is either right or wrong, it all makes sense and as long as you follow the rules everything will be ok. Right? Umm… no.

### Here are my **Ten Commandments of Maths**: all were considered to be obviously correct at one time but, as we shall see, rules are made to be broken.
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### John Venn did not invent the Venn Diagram (the original idea was __Euler’s__). But he is famous for popularising the diagram which now takes his name. Mathematicians are always looking for ways to make abstract ideas easier to picture – like the Number Line for “picturing” numbers, or the Bar Chart for picturing data. Venn Diagrams are a beautiful way to organise groups, or “sets” of objects.

**A FUN EXAMPLE:** suppose we want to sort these items into “things with exactly four legs” (Set A), and “the rest” (not in Set A):

John Venn, zebra, cat, octopus, tripod, chair.

One way to do this would be to split them into two lists, but a far prettier way is to arrange them into a Venn Diagram with one circle:

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### This handsome chap is Frenchman Rene Descartes (1596-1650), who famously said “I think therefore I am”.

If you’re thinking about what he might mean by this, then it apparently means you exist – great news and congratulations!!

But the reason Descartes is my “hero of maths” for this month is because he also gives his name to **CARTESIAN GEOMETRY** – which is what you do when you plot the point (4,3) on a graph by going “along the corridor and up the stairs”. By the way, “**Geometry**” is a posh word for “**Shapes**”.

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__THE HEXAHEDRON AND OTHER HEX WORDS__

Every school child knows that a Hexagon is a flat shape with six straight sides, but here are six more great Hex- words to enjoy, together with instructions on how to make your own Hexahedra!

1) HEXADACTYLY: the condition of having six fingers (or toes) on one (or both) of your hands (or feet). King Henry VIII’s second wife Anne Boleyn was hexadactyl, meaning that you could count all six of Henry’s wives on the fingers of one of Anne’s gloves.

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In the UK, we use a unique mish-mash of Metric and Imperial systems for measurements. For example, petrol is sold in litres (Metric), yet fuel efficiency is measured in miles per gallon (Imperial). Milk is sold in litres, but beer in pints. And during the 2016 Olympics, I even heard a bizarre TV athletics commentary that a long jump was… :

This mess needs clearing up, so let’s decide here and now which is better: Metric or Imperial?

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**How many gifts did “my true love give to me” in the traditional song?**

For anyone unfamiliar with the song:

“On the first day of Christmas my true love gave to me: a Partridge in a Pear Tree”: 1 gift.

“On the second day of Christmas my true love gave to me: Two Turtle Doves and a Partridge in a Pear Tree”: this is another 2+1=3 gifts, so 4 gifts in total so far.

On the third day I’m given Three French Hens, a further two Turtle Doves, and another Partidge in a Pear Tree; so 3+2+1=6 gifts on day three, making 1+3+6=10 gifts in total so far. The song continues all the way to “12 Drummers Drumming” on day 12.

The keys to working out the total number of gifts over all 12 days are the **Tetrahedral numbers**, which are made up from the **Triangular numbers**.

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__Ten Things To Do with your New Five Pound Note__

By now most readers will have seen the new five pound note: made of polymer plastic and featuring Sir Winston Churchill on the reverse. Here are ten fun things to do with your new fiver!

1) See how many times can you fold it in half. The new fiver is designed to be crease-resistant, which makes this challenge even harder. I’ve managed 5 folds so well done if you can manage more! The world record for folding a piece of paper in half is 12 times set by Brittney Gallivan while she was still at High School, but that was starting with a really really long piece of paper (1.2 kilometres long!).

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In June of this year I bought a 60cm ruler from eBay. It arrived promptly – in a HUGE cardboard box measuring 80cm x 40cm x 20cm! I posted a photo on Facebook, and before long the National Media got hold of the story, which was then published in the August 5^{th} editions of both the Daily Mail and the Sun newspapers. The story was even discussed on Channel 5’s “The Wright Stuff”.

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