Math Is Fun Forum

elliewellie

Member

Registered: 2012-04-15

Posts: 1

maths challenge

I want to work out how many £1 coins fit into a circle of 1 metre in diameter. Can anyone help?

mathmatiKs

Member

Registered: 2012-04-14

Posts: 45

Re: maths challenge

Hi.
You would have to first find the diameter of the coins and the area.

I don´t have any formula. Sorry

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"... And as we let our own light shine, we unconsciously give other people permission to do the same. As we're liberated from our own fear, our presence automatically liberates others."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: maths challenge

hi elliewellie

Welcome to the forum!

This is not an easy question to answer.  You will have noticed that when you push the coins against each other you get gaps that cannot be filled.

The best packing arrangement involves having six coins around  a coin at the centre and working out in a sort of hexagonal type way.

Did those nasty teachers give you this as a holiday project?  'Cos you've left it a bit late to get an answer. 

Put as many coins as you can afford in a straight line against a ruler and see how long this line is.  Then divide by the number of coins and you'll get a good estimate for the diameter.  This'll sound good in your write up as you've used measurement and averages already.

Do you know the formula for working out the area of a circle?

Because (area of big circle) divided by (area of little circle) would give the answer if the packing was perfect with no gaps.

As there are gaps it will only give you an 'upper bound' ie. The true answer must be less.

So now we need to estimate how much to allow for the gaps.

You could make a much smaller circle, pack it with coins and count them.  Then do the area trick to work out the upper bound for that circle.

Now I haven't done this so this is NOT the value, but let's say you calculate that there's 20% lost in the gaps.  Scale that up and you've got a reasonable answer to hand in.

My guess (and if I'm wrong then I'm sorry) is that your teacher doesn't actually know the answer either.  He/she just wants you to come up with some sensible maths on the way to an answer.

You'll be able to put in words like area of circle, packing, hexagons, divison, diameter, average, upper bound, estimate, percentage ......

If I was your teacher I'd be pretty impressed by that lot and give you a top mark.

Post back if you need more help with any of this. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ljw5021

Member

Registered: 2012-04-23

Posts: 1

Re: maths challenge

Bob pretty much nailed it. I imagine you might be able to get a decent approximation if you could think of a hexagonal packing and extrapolate it to inscribe the hexagon in the circle. You'd have a lot less area to estimate on, then. I agree that your teacher is probably just looking for a decent thought process on how to approach the problem.

This sounds like a Google interview question, by the way. Similar to "How many golf balls can fit on a school bus?"

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: maths challenge

Hi ljw5021

Welcome to the forum!

No reply from our poster however. 

cynical view:  We may have to wait until next Easter. 

btw.  How many golf balls will fit on a school bus?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: maths challenge

Hi Bob

When you mention golf balls on a bus-look at my "Fermi's questions!!!" thread.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: maths challenge

hi Stefy,

I looked through all 5 pages of it and found no golf balls. 

But I did see my name mentioned.

I can confirm that Your Highness should be used for both male and female Royalty.

You'll notice I have used capital letters.  It is important, when addressing Royalty, that you include the capital letters.

Now you might be wondering how you say a word with a capital letter.

It's easy if you remember your history lessons.  In the past Royalty could just wave a finger and you'd get your head chopped off.  Once you remember that, the capitals come easily. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: maths challenge

Hi Bob

I was talking about the concept.But I may add the golf ball questions if you want to.

Thought so,but wasn't sure.Does the Queen still has as much power as in the past?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: maths challenge

No, very little!

She has to open each new parliament and read a speech, but it gets written for her by the prime minister's team.

When a new act of parliament is passed, she has to sign it to make it 'official' but she has no choice.

When a government has to call an election, she has to formally 'dissolve' the old parliament, but again she has no choice.

In other words, her role is totally ceremonial.

That's why she continues to be popular; she cannot be blamed for anything that governments do that upset people.

I suppose it's a bit like a country's flag or national anthem.  You honour it but you cannot dislike it.

And they say she earns the country lots of money because of the tourists.

These days, the Royal family is often the target for comedians.  They don't tend to heckle back!

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: maths challenge

Thought so. You haven't told me if you liked the K5 nickname.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: maths challenge

You haven't told me if you liked the K5 nickname.

Don't understand.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: maths challenge

Look at your av.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.