# Wrong, But Useful: Episode 2

It’s a new month, which means it must be time for a new episode of Wrong, But Useful!

This time around, we talked about queuing at EuroDisney, how to play Battleships, why Peppa Pig’s dad has a quadratic equation in his office, 110%, elliptic curves and Dave’s brilliant new game.

The puzzle:

I have three indistinguishable coins: one always comes up heads, one always comes up tails and the third is a fair coin. I pick one of the coins at random and toss it twice and get the same result both times. What is the probability I picked the fair coin?

What I don’t understand:

Why matrix multiplication works the way it does.

## Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

### 41 comments on “Wrong, But Useful: Episode 2”

• ##### Dan Pearcy

Hey guys,

Good work with starting a podcast – I agree that it’s nice to hear people ‘ramble’ (in a good way Dave) about maths.

In terms of understanding the formula for the volume of a pyramid – is the use of calculus not the easiest way to do it? Maybe you want something that all Secondary students can understand? Colin was referring to this with splitting the volume up into an infinitesimal slabs so I guess that’s the main idea behind the mathematics at least.

The “3 points on the surface of a sphere problem” is interesting. At first I wasn’t sure if I agreed but with more thought (actually with an onion to draw points on) I’m coming round. My mind at first could only cope with the 2-D equivalent which of course isn’t true – the 3 dimensional aspect is initially aukward to get your head around.

Thanks for some thought provoking ideas,

Dan

• ##### Colin

Thanks, Dan!

Oh, 3D calculus is certainly a good way of doing it – but you’re quite right, trying to keep it to more simple methods was an implied part of the brief! You win a spotter’s badge for catching me slip in some calculus by the back door, though 🙂

• ##### Dave Gale

Thanks Dan.
I knew ‘rambling’ was a positive phrase. 🙂
I’m always looking for intuitive answers where possible so going straight for 3D calculus is something I’ll avoid. Colin’s suggestion is fairly neat and I can see how it’s sneakily calculus if you make the layers very thin. I’m still interested in other ways of thinking about it though.
I like the sphere question and hadn’t even thought about the 2D version. 3D gives 3 points is certain. 2D gives 2 points is certain. So I conjecture that in four dimensions, 4 points picked at random on a *don’t know the name* shape will certainly lie in the same *half of the shape of which I don’t know the name*.
Hmm, now how do I prove that?
Thanks Dan.

• ##### icecolbeveridge

@Dave Gale It’s a hypersphere… and I don’t know if it’s a hyperhemisphere or a hemihypersphere :o)

• Pingback: Wrong, but useful | cavmaths

• ##### Joshua Zucker

One of the, um, better explanations for why matrix multiplication works the way it does is at http://betterexplained.com/articles/linear-algebra-guide/ … is that the kind of thing you’re looking for?

I’d love to talk about matrix multiplication more. It’s one of my favorite operations.

• ##### Colin

Oo! That looks great. Thanks, Joshua!

This site uses Akismet to reduce spam. Learn how your comment data is processed.