Strings Around the World...

I could some err with calculations , but I 've got something like 8 metres to add.

In any case I was aware of this problem as result looks like incrediebly small. But math is math.

About ⁴⁴/₇ metres.

Yes I believe your answer is more accurate as expressed in rational notation. I do not know who invented this problem, but it's more psychological then math. When I was a student this problem test had been passed if student voice number less than 10 m. Most of them in stress situation couldn't believe that it could be so small and tried to find mistake at his calculations or even voice result multiplied on 100 or 1000 pursued their good luck.

Kind regards.

I also heard this one a long time ago. Amazing how many people just refused to believe it, even though the maths is very simple.

Regards,

John

710 / 113 is more accurate. (355/113 is a better approximation than 22/7)

With that solved. How far from the equator should you be to have the same string 1 metre above the (theoretical) ground?

"710 / 113 is more accurate" - I reckon the difference is about 2.5mm - that's 6 x 10^-9% of the overall length. Some string!

For the other question, I make it about 2.5km, but I could be grossly out!

Just drew it to scale on AutoCAD - it came up with 488mm @ 2.5km - so I guess I'm in the right ball-park.

Taking the equatorial radius as 6378000 meters I make it about 3572 meters. d = √(2R)

Hello Lapinbleu

That problem, or different versions of it, is a very old one.

The simple but approximate answer can be worked out in one's head, of course.

As far as I know, the Number Π (Pi) has yet to be fully defined, which is why any answer is only ever approximate.

Kind Regards....

It is actually scary! The overlap during the tsunami were 22 metres and the diameter of the earth reduced by 7 metre.

...but here's some curiouser magick... (until you think it through)

If you did the same experiment on a planet with a circumference 10 times that of the earth (starting with a 400,000 Km piece of string) - how much extra would you need then?

The same as for a planet with a 1km radius.

Is this the origin of the string theory?

In fact it is the reason why string theory is a theory... in practise they can't get the damn string to stay exactly a metre off the ground (of course because the American contingent of the team won't work in metres).

How rude of them! Maybe they should work on the English rood (12') then they will clear the waves ruled by the British (As in "Britain wave the rules") and the dam string won't shrink anymore and cause a discrepancy of 2.5 mm.

Further to your planet example. The difference in length round a soccer or tennis ball will be the same. You however can't use a cricket ball (It will move when you tickle it)

How many fortnights do we get to make our decision?

Hey, I represent that statement...

But you are right we don't work in metres, nor do we work in meters but we are going metric, we are just doing it inch by inch.

(BTW you will notice that when I use measurement units in a post I generally use metric units. I consider myself a renaissance man, and can speak in many units...)

The problem is with different units with the same name.

In SA we had cape feet and imperial feet (the ruler that came in walked in the water and his shoes got wet and stretched)

Gallon US and imperial,

The rest of the world has it easy.

Here in Canada, we are officially Metric, but our biggest trading partner, directly south of us, is Imperial.

So by necessity, we have to be thoroughly bilingual, measurement-wise.

Possibly even schizophrenic.

I'm not even going to mention fractions, but I am.

What? Do you mean Mexico, because as far as we're concerned, you're our Northern states... So Obama or Clinton?

MUNKY SIT TIGHT STOP IMPERIAL GUNSHIP ON WAY ENDS

How long is a piece of string?

Kind Regards....

It's this long.

No it's not! It's this long. Wanna bet?

You're going to carry a ball of string that big, all around the world ? At one metre high ? I say it can't be done. Your arms aren't big enough.

Try carrying this one Kris.

Of course; d being the diameter of the sphere:

Pi*d=x

Pi*d+2=x+Pi*2

Don't need that d then: Nor the x, for that matter...

44/7 m. And that whether it's a billiard ball or a galaxy.

I like the way this one baffles students - it's counter-intuitive, but the four million yards don't even come into the equation...

2π(r+1)-2πr looks nicer.

2 Pi metres

OK. So how long would the string have to be if we cut a channel around the World to the center of the Earth, wound it several times and considered it a yo-yo that would be used by a giant located somewhere in the center of the Sun?

Folks, these questions need to be answered!!!

"To follow, without halt, one aim: there's the secret of success" -- Anna Pavlova

Wasn't that Pavlov's dog's girlfriend?

NO vermin..............that was Skinner's Rats!!!!!

...............and you know what we do with them!!!!!!

Hmm ... The String Thread ... there's a nice ring about that.

Untangle this piece of string.

While the math is trivial if we ASSUME a smooth sphere, how does the value change if we would follow the true line around the earth? (ie: if we added the lengths of the hills and valleys). Seems more like a problem for Chaos Theory. Any Comments?

Yes.

Simply done. Provided the string followed the countours always VERTICALLY above the surface the extra length would still be 2 Pi metres.

This is only a theoretical exercise, and as you would need about 50M/100M people to support the string 1 metre above the surface all around earth, at any overhanging cliffs the string would theoretically be underground. Two thirds of the supporters would have to be able to swim.

Is there any simple circumference around earth that would be clear of buildings, chimneys, to avoid using climbing ropes? Can we stop the traffic, ships, locomotives, aircraft landing while this is being demonstrated? When measuring, should we correct the length for stretch, humidity, temperature?

All the upsies, and all the downsies might lead to the same result, but it what we compared. According to this, average elevation is 2000m below sea level. If we compared a circle of string at sea level with one that followed solid contours, we'd need a lot more string*. Little people could go up and down the grains of sand with very small string and go on forever if they were small enough.

* It would have to be very strong, to avoid breaking under it's own weight when it drops down big vertical bits. Working out the limitations in air wouldn't be too hard, but I don't know if the string has any bouyancy when it drops down the Marianas Trench. I suppose it depends how damp a soggy bit of string is.

Hello Lapinbleu

There is a major problem if string of any type is used.

With fluctuating humidity and temperature, the apparent length of the string alters appreciably.

I offer the above explanation, as my humble opinion.

As the old saying goes: "It's not the Heat, it's the Humility".

Kind Regards....