Maths help two :)

Orionaut

Orionaut

Orionaut

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The other thread just reminded me of a question I saw many years ago (In New Scientist IIRC)

Consider the situation...

Imagine a string wrapped all the way around the Earths equator.

Now imagine a second string raised to a point 1M above the earths equator.

Q: How much longer is the second string than the first.

I am not searching for the answer here, simply the method.

What was your solution, and how did you arrive at it?

;) :p
 
Orionaut said:
The other thread just reminded me of a question I saw many years ago (In New Scientist IIRC)

Consider the situation...

Imagine a string wrapped all the way around the Earths equator.

Now imagine a second string raised to a point 1M above the earths equator.

Q: How much longer is the second string than the first.

I am not searching for the answer here, simply the method.

What was your solution, and how did you arrive at it?

;) :p
Click to expand...
(2*pie*[r+1]) - (2*pie*r)

Where r is the average radius of the earth in metres at the equator.

But if you want to lay the string flat against every nook and cranny of the earth to get a true measurement, good luck :P
 
D3K said:
(2*pie*[r+1]) - (2*pie*r)

Where r is the average radius of the earth in metres at the equator.

But if you want to lay the string flat against every nook and cranny of the earth to get a true measurement, good luck :p
Click to expand...


Correct, but too complicated.

There is a simpler way of looking at it ;):p

Thats what I am looking for, not the solution but rather the logic.

:)
 
The equator doesn't have any altitude. There's no such thing as "1 metre above the equator"?
Is it 1m above sea level at the equator or 1m above ground level? They're going to be very different things.
 
touch said:
The equator doesn't have any altitude. There's no such thing as "1 metre above the equator"?
Is it 1m above sea level at the equator or 1m above ground level? They're going to be very different things.
Click to expand...
It's a problem to demonstrate that to calculate the change in circumference of a circle as a result of change in diameter/radius doesn't require you to know the original circumference or diameter/radius.

You're looking at it too literally if you're worrying about sea level vs ground level.
 
Orionaut said:
Correct, but too complicated.

There is a simpler way of looking at it ;):p

Thats what I am looking for, not the solution but rather the logic.

:)
Click to expand...
You want me to factorise it?

2*pie*(r+1/r)

Kenai said:
It's a problem to demonstrate that to calculate the change in circumference of a circle as a result of change in diameter/radius doesn't require you to know the original circumference or diameter/radius.

You're looking at it too literally if you're worrying about sea level vs ground level.
Click to expand...
You need to know the radius to calculate the specific change. Even if you don't know it, radius/diam is still required in the equation.
 
D3K said:
You need to know the radius to calculate the specific change. Even if you don't know it, radius/diam is still required in the equation.
Click to expand...

If you want to demonstrate working from first principle maybe but once you know that all the original figures drop out, it means you can happily calculate the change in one of those numbers simply by knowing the change in the other.
 
Kenai said:
If you want to demonstrate working from first principle maybe but once you know that all the original figures drop out, it means you can happily calculate the change in one of those numbers simply by knowing the change in the other.
Click to expand...


All the information required is in the question. ;)
 
Kenai said:
I was trying to post in a way that didn't just kill the thread half a dozen posts in :p
Click to expand...


True

That was my logic when I first saw it. I haven't been told what the earths radius is, therefore it doesn't matter

Once you accept that, the answer is clear.

It is a bit like the "Monty hall" problem.

People feel the need to come up with all sorts of complex arguments to explain how this, apparently, counter intuitive situation can arise.

In fact it isn't complex at all.

The solution is that it has little to do with probability and everything to do with the fact that the game show host knows which doors have the car and which have the Goat!
 
btw, when you said 'raised to a point 1m above the equator' I thought you meant towards the North Pole, with the second string then being smaller, still wrapped round the earth....missed the fact you said the second string would be bigger!
 
D3K said:
pie pie
Click to expand...

D3K said:
pie
Click to expand...

D3K said:
pie
Click to expand...

iQM0O9W.png
 
D3K said:
(2*pie*[r+1]) - (2*pie*r)

Where r is the average radius of the earth in metres at the equator.

But if you want to lay the string flat against every nook and cranny of the earth to get a true measurement, good luck :p
Click to expand...
That’s what I thought so I’m intrigued as to what the super duper concise answer is.
 
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