I bet you do not belive this!

Imagine you have a very long piece of string. It's long enough to stretch all the way around the earth.

Since the circumference of the Earth is about 40,074 kilometres, that's how much string you would need.

Imagine that you lay out this string along the ground and on top of the oceans, all the way round the Earth.

That's one long piece of string!Now pull it tight, so it lays flat. The string makes a big circle that is 40,074 kilometres, or 4,007,400,000 centimetres long.

Then you realize that you have an extra metre of string in your pocket, and you want to add it to the string around the Earth ...

You'll have to cut the circle of string somewhere, as it passes in front of you on the ground. Then you'll add exactly one metre more string.

Now you want to spread out this extra bit of string around the Earth, supporting it somehow, so that the string forms a circle off the ground, all 40,074 kilometres (plus one metre) around the world.This may take a while! But eventually, you've smoothed the string out into a perfect circle, all the way around the Earth, and slightly off the ground because of the extra 100 cm you added.

Here's the question I want to ask you ...

How high off the ground would the string be?You would probably say that the string will hardly be off the ground at all. After all, you only added 100 cm, and the string's length was 4,007,400,000 cm to start with. Most people guess something like 0.00005 cm.The very surprising answer is that the string will be 15.9 cm off the ground, all the way around the Earth!If you think about it, this is a very large distance for so little change to the total length of the string!Another way to look at the problem may make the answer seem more reasonable. The height of 15.9 cm is in addition to the radius of the Earth. Since the Earth's radius is about 637,800,000 cm, the change in height is in fact very tiny.But wait, there's more ... The size of the object you're wrapping the string around is completely irrelevant to the problem!

Imagine wrapping a string tightly around a basketball, which has a circumference of about 94 cm

Then you add exactly 100 cm of string, and smooth out the circle all around the ball.

You will make the surprising discovery that the loop of string is once again 15.9 cm above the ball!

Whether the ball is the Earth, or a basketball, or a marble, adding one metre of string to the circumference will make the string form a loop 15.9 cm above the surface, regardless of the size of the sphere the string is wrapped around! These surprising results may be more believable once you see the answers worked out.

Proof I hear you shout! well here it is,

Here are the calculations that show the height of the string above any sphere, after you add one metre.

We'll make the radius R, and the circumference C.

This will be a proof that it works for any values of these measurements.

We added 100 cm to the circumference, making the new longer length of the string C+100 cm.

Next, we solved for the radius of this new bigger circle.

After some simplifying, you can see once again that the new radius is bigger by exactly 15.9 cm.

Because we did this without specifying values for R and C, it is a proof that it will work for any sphere.

so now you know!