Americans, Math Says “Your Next President Is….”

[This is a back issue of this site’s newsletter. It was originally sent out in August 2015, but only published online in June 2016]

Remember last week’s email, about elections? If there are two major parties in an election, they both tend to be centrist. That’s because if one shifts left or right, it ends up losing votes to the other. Continue reading Americans, Math Says “Your Next President Is….”

Time Travel, Truth and the Color Of My Shirt.

Have you ever played “truth and lies?” It’s an icebreaker game where you make three statements – two are supposed to be true, and one false. It helps people in a group to get to know each other, and see how well they already do.

Well, next time you play, you might like to bend it into a mind-twisting IQ puzzle.

Continue reading Time Travel, Truth and the Color Of My Shirt.

Movie Ticket Puzzle Solution

[This is a back-issue of one of this site’s newsletters]

It’s Monday Morning Math Time!

If you’re hungry, have a look at this yummy breakfast math video. You’ll see there’s more than one way to cut a bagel, and maybe learn a bit of topology too.

I promised to give you a solution to the movie ticket problem.
If you missed it, have a read here and see if you can solve it before you read on here!

Continue reading Movie Ticket Puzzle Solution

1 and 0.99999….

The other day, this old familiar topic came up: how can 0.99999…. equal 1?

Now, there are plenty of sites dedicated to proving that these numbers are equal. However, these proofs clearly aren’t enough for some people. It doesn’t feel “right” in their gut that this recurring decimal should equal that whole number.

Perhaps that’s how you feel too.

If so, let me ask you this: is 2/5 the same number as 4/10?

Now, they look quite different. Sometimes, in practice, they are quite different – I can imagine it might sometimes make a difference if a pizza is sliced into five slices or ten, even if the amount of pizza eaten is still 40% of the original whole pizza.

Nonetheless, 2/5 and 4/10 are the same number. Or rather, they represent the same number – a point on the real number line, a bit less than a half, a bit more than a third… We say these fractions are “equivalent”, and that two fifths “equals” four tenths.

On the other hand, 2/5 and 4/10 look very different. The two fractions take up different amounts of pixels on your screen. Yet, we’re happy to accept that they are equal.

One way to resolve this – the correct way, actually – is to say that the fractions themselves merely represent a number. They are the language we use to talk about the number. However, the number is an abstract thing that exists quite apart from the symbols we use to write it down.

Ceci n'est pas un chat
Ceci n’est pas un chat

If I write the letters C, A and T in that order, your mind is filled with purry furry goodness. However, cats exist quite apart from the word we use for them. And words can never perfectly capture the concept of a cat. (And different words can be used to represent the same concept, but we don’t complain about that.)

Nobody thinks that a cat is the same thing as the word spelt C-A-T. Why should a number be the same thing as the text we use to write it down?

Scribbles on a page aren’t numbers, even if they represent numbers. This is true, whether they are fractions or strings of decimal digits. And just as many different fractions can represent the same fractional number, there is sometimes more than one string of decimal digits that represent it too.

We aren’t taight this in schools. We are taught “0.4” is a number. “0.3333333….” is a different number.

Then we meet “0.3999999….”, which is clearly a different string of digits from “0.4”. However, they represent the same abstract number that 2/5 and 4/10 do.

You can do arithmetic with strings of digits. If you do arithmetic with 0.39999…. and 0.4, you get no weird surprises if you believe them to represent the same number. If you insist they must be different, though, arithmetic starts to behave in strange, hard-to-understand, counterintuitive ways.

Your Ancestor, Julius Caesar.

[This is a back-issue of one of this site’s newsletters]

I got an interesting question by email the other day.

It was from someone who had just read my rice and chessboard page. That’s the story about a king who offered a reward to the man who had taught him the game of chess. Have a read!

Here’s the question that was asked:

Continue reading Your Ancestor, Julius Caesar.

60 Degrees?

[This is a back-issue of this site’s newsletter]

Saw these online, thought I’d share them with you all –

  • Parallel lines have so much in common. It’s a shame they’ll never meet.
  • I took the shell off my racing snail, hoping it would make him faster. If anything, though, he just become more sluggish.
  • How do you think the unthinkable? Why, with an itheberg, of course!
  • I tried to catch some fog yesterday. Mist.
Badum-tsss! And it’s time for Monday Morning Math!

Continue reading 60 Degrees?

Pythagoras, Venn, Euclid and Complex Numbers

[This is a back-issue of one of this site’s newsletters]

Last week, I showed you how a puzzle about rectangles gives you a simple formula for pythagorean triplets. This week, I want to show you a bit more about that formula.

But first, have you seen this? It’s proof that even people in a marketing career need to know a bit of mathematics:

Continue reading Pythagoras, Venn, Euclid and Complex Numbers