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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.

### Links!

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.

Wrong, But Useful: Episode 2 http://t.co/Gx5PkVmGF9

Episode 2 of #WrongButUseful http://t.co/9j2OzfOtQf inc battleships, elliptic curves and queuing #mathchat

Episode 2 of #WrongButUseful http://t.co/9j2OzfOtQf inc battleships and queuing #mathchat @srcav @aap03102 @singinghedgehog @JusSumChick

Episode 2 of #WrongButUseful http://t.co/9j2OzfOtQf inc battleships, elliptic curves and queuing #mathchat @aperiodical @inquirymaths

@reflectivemaths Of course, @icecolbeveridge should be ‘selling’ this post rather than/as well as you! #mathchat

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

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 π

Thanks Dan.

I knew ‘rambling’ was a positive phrase. π

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.

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

Episode 2 of #WrongButUseful http://t.co/9j2OzfOtQf inc 110% and a new game #mathchat

Great podcast on queuing from @reflectivemaths: Episode 2 of #WrongButUseful http://t.co/ZaMfnaF5DJ @ORinSchools – worth a listen

Episode 2 of #WrongButUseful http://t.co/9j2OzfOtQf inc battleships, elliptic curves and queuing #mathchat @tesMaths @Maths_Master

From @reflectivemaths: Episode 2 of #WrongButUseful http://t.co/RihWHXuOB7 inc battleships, elliptic curves and queuing #mathchat #maths

Wrong, But Useful: Episode 2 – Flying Colours Maths | Flying Colours Maths http://t.co/PLnnLKstBc alternative to math maths, should be good

Episode 2 of #WrongButUseful http://t.co/9j2OzfOtQf inc battleships, elliptic curves and a new game @ilovemathsgames @EmathsUK

Episode 2 of #WrongButUseful http://t.co/9j2OzfOtQf inc battleships, elliptic curves and a new game

Episode 2 of #WrongButUseful http://t.co/9j2OzfOtQf inc battleships, elliptic curves and a new game @fullonlearning @jamesgurung

Episode 2 of #WrongButUseful http://t.co/9j2OzfOtQf inc battleships, elliptic curves and a new game @GarrodMusto @r_hopes @hegartymaths

Episode 2 of #WrongButUseful http://t.co/9j2OzfOtQf inc battleships, elliptic curves and a new game @StudyMaths @Just_Maths @bluecombats

Podcast? RT @reflectivemaths: Episode 2 of #WrongButUseful http://t.co/PLnnLKstBc inc battleships, elliptic curves and a new game

Interesting comments about #WrongButUseful episoe 2 from @DanielPearcy #mathchat http://t.co/qfdWUupHSd

Also @colinhegarty Shameless promotion of the #wrongbutuseful podcast http://t.co/lpWqj6pymb π

Chuckled along to @icecolbeveridge & @reflectivemaths’ #WrongButUseful ep 2 f. battleships, elliptic curves & queuing http://t.co/Vh1JiCv8N5

Wrong, but useful ep 2. Superb maths podcast. http://t.co/vlvAg2UY1o @reflectivemaths @icecolbeveridge

[…] Colin’s a maths tutor and writer and his blog has lots of things about maths in general. Also the host site of a wonderful maths podcast called Wrong, but Useful (episode 1 and episode 2). […]

[…] second episode (http://www.flyingcoloursmaths.co.uk/wrong-but-useful-episode-2/) started with a theme tune, which was great, and the maths behind it was pretty interesting. The […]

[…] was sent to me via Twitter by Will Davies (aka @notonlyahatrack) who had listened to the podcast Wrong, But Useful (by Colin Beveridge, aka @icecolbeveridge) and attempted the following […]

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.

Oo! That looks great. Thanks, Joshua!

RT @reflectivemaths: #wrongbutuseful Previous episodes:

http://t.co/WfwFbFY5eE

http://t.co/rkCXMzmuDS

http://t.co/ngLw2iEw2M