# Maths help two :)

Discussion in 'General Discussion' started by Orionaut, Apr 21, 2019.

1. lunar

# Location: London

Your equation above is what I thought it would be too. However, I was reluctant to respond because I think there is more to the question than meets the eye.
I recall a similar question been asked in Dr Kharl's radio 5 Science phone-in.

2. esmozz

# Posts: 197

Technically he's asking about the great circle on a spherical earth which corresponds to the equator. If the earth is not spherical then the calculation may be different.

The WGS84 datum is reference oblate spheroid used to define the earths surface. It was my understanding that using this datum the earth is defined to approximate a ruby ball, making calculation different. However having just checked it again I may well be wrong, in which case you can ignore everything I've written previously.

Also, since I'm going to be awkward, the answer is 1m (give or take). I got this by drawing a slice of pie and marking the two radii, the earths radius is so huge compared to the difference between the two radii that the end approximates a box 1m square. Hence 1m. I have no idea if this is a good answer.

Edited to add: Having thought about it a bit more, I think it's a rubbish answer. I'm going to give up now.

3. h4rm0ny

# Location: Yorkshire and proud of it!

I think they meant floating magically above the first string at the same latitude, rather than lying on the ground slighty North of the first one.

I'd be fascinated to know how you could do that, as the question is "how much longer". It's asking for an absolute value (e.g. 400km) so we need an absolute value to insert into the formula. I.e. the diameter of the Earth.

Yes, it's an oblate spheroid. But that doesn't make any difference unless we're talking volume. Any given lateral cross section is still going to be a circle (give or take some mountains).

4. Kenai

# Posts: 19,146

If the radius increased by 1m, the circumference increased by 6.28m. It doesn't matter whether you started with a basketball, the moon, the earth or the sun. The answer will always be the same.

5. esmozz

# Posts: 197

Surely if you took a circle round the poles, i.e. normal to the equator you would get an oval. Not that it makes any diffence here.

So 1m then (give or take)

6. h4rm0ny

# Location: Yorkshire and proud of it!

Someone can shoot me now, please. I wont object.

Equator was specified. That is a measurement at a specific latitude.

7. FoxEye

# Location: Cornwall

Not that I care. Maths sucks donkey balls.

8. Kenai

# Posts: 19,146

I think you're pushing it a bit to say that 6.28 is 'give or take' the same as 1

9. Crpwned

10. esmozz

# Posts: 197

I dunno, over 6400,000m its not bad.

Hard to argue against that so i won't.

I think the point I was originally trying to make was (and I've had to go away and check since it was 20 odd years since I studied this, so I may still be wrong) that the surface of the earth can be represented mathematically by a geoid based on the WGS84 datum. That geoid is an irregular surface, nonetheless, at the equator you could approximate the circumference using a mathematical series (up to n = as high as you like) - it would not be a circle.

However all I seem to have proved is I completely missed the point of the original question. Also:

11. LuckyBenski

# Location: London

This thread made me feel really smart until I failed to account for the 1m applying to both sides of the earth, and so the answer is 2π and not just π

12. lunar

# Location: London

Ironic, where would we be without Maths (and Physics)?
No Internet, no TV, no mobile phones, no satellites, no radio, no mains electricity.......

13. Angilion

# Location: Just to the left of my PC

It's also only just an oblate spheroid. The question treats the surface of the Earth as being smooth. Treating Earth as a sphere is an approximation in the same ballpark as that.

I have to admit that my initial thought about the answer was that the outer rope would be much longer than the inner one, hundreds of kilometres longer. I felt a bit silly when I read the correct answer and realised that yes, of course that was the correct answer. I've known the formula for the circumference of a circle for a very long time and should have gone straight to the correct answer.

14. D3K

# Posts: 3,006

Post #10 on the front page

15. FoxEye

# Location: Cornwall

Subjective post was subjective.

It's hard and I'm not very good at it. Ergo it sucks balls

16. Double07

BEER

17. dl8860

# Location: Surrey

How can you say these words and then go on to talk about oblate spheroids. Are you clever or not?

18. h4rm0ny

# Location: Yorkshire and proud of it!

I am usually very clever but occasionally can make statements without thinking things through and which are cripplingly embarrassing sometimes.

Example above.

19. Illgresi

# Location: Perth

1/r times bigger

or

100/r expressed as a percentage.