Math Is Fun Forum

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

“Only Connect”

On “Only Connect” last evening, the Mathematicians were playing agains the Wordsmiths. The Mathematicians won!

“Only Connect” is a series of word-quiz game shows currently being shown on Mondays 20:30–21:00 on BBC Four. I was surprised the Mathematicians took ages to work out the value of

. And there was a slight mistake on the show.

is not

but

where

is any integer.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: “Only Connect”

The mathematicians were surprised at themselves too. Presumably the pressure was getting to them a bit.

The mistake that I was more annoyed at was when the show said that ≡ meant "equal by definition".

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Why did the vector cross the road?
It wanted to be normal.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: “Only Connect”

Hi mathsyperson;

  I have seen ≡ as meaning an identity or exactly equal.

Last edited by bobbym (2009-07-21 07:49:14)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: “Only Connect”

Yes, that's how I know it as well. "Equal by definition" is different though.

≡ is used for statements like (x+1)² ≡ x² + 2x + 1.
They're identical as opposed to equal, because the value of x doesn't change the validity.

Equal by definition , :=, is used to 'shorthandedly' define a new variable.
Let's say I want to use a function given by that expression.

I could say "Now consider the function f, where f(x) = (x+1)²"
Or instead, "Let f(x) := (x+1)² ≡ x² + 2x + 1."

:= and ≡ are two different things.

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Why did the vector cross the road?
It wanted to be normal.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: “Only Connect”

HI mathsyperson;

Yes, I agree. I wasn't agreeing with the show. Your clarification did make the point clearer to me.
Thanks.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: “Only Connect”

And there was a slight mistake on the show.

It all depends on which leaf you choose, but the standard one is to make the value pi.

The mistake that I was more annoyed at was when the show said that ≡ meant "equal by definition"

I've seen this used by a few professors.  I don't see anything wrong with it.  Different people take symbols to mean different things.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

davidbod

Member

Registered: 2009-08-13

Posts: 1

Re: “Only Connect”

The mistake that I was more annoyed at was when the show said that ≡ meant "equal by definition".

During my maths degree I found that different lecturers, books and countries didn't have a standard for this (as http://en.wikipedia.org/wiki/Table_of_mathematical_symbols shows).

As for (2n+1)pi, I guess this is true but idea is that the team are looking for the connection between the clues so the answer they should give is that they are all things that *can equal* pi.

I'm glad you're watching the show. I do my best to give maths questins a fair crack of the whip as I feel it's a subject that's under-represented (or, worse, badly represented) in other quiz shows.

Kind regards,

David
OC Question Setter/Editor

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: “Only Connect”

Hi davidbod;

  Great that you noticed this forum.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.