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.
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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!
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Here’s a puzzle for you to try – how creative can you get while solving it? Continue reading Movie Tickets and Time Machines
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.
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.
If you visit sites like this one, you can see maps showing which parts of the earth are sunlit and which are in darkness. Normally the maps look something like this:
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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:
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There’s a new game on Dr Mike’s Math Games for Kids – OgleBoro City. The game is not my invention, it’s the brainchild of Mac Oglesby. Mac spent decades as a teacher, coming up with creative teaching resources. Then, after he retired, he kept doing the same!
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Saw these online, thought I’d share them with you all –
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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
[This is a back-issue of one of this site’s newsletters]
If you’ve been reading for a while, you might remember this puzzle: Can you find a rectangle whose area equals its perimeter?
For example, a 6 x 3 rectangle has a perimeter of 18 units, and the area is 18 square units. The same number!