# String around the earth - episode 171 no such thing podcast

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 1242384.  Thu Jul 13, 2017 6:05 pm I am not the brightest and find that I am confused by a fact mentioned in episode 171 of the no such thing as s fish podcast. It was stated that if a piece of string that just stretched around the earth was increased in length by three feet it would then be able to clear the surface by just under six inches. An amazing fact! However, and this is where my limited brain could not keep up, it was then stated that the was a phenomenon that occurred regardless of what a piece of string is wrapped around, the example quoted being a person's waist. I have tried wrapping a piece of string around my waist and then increasing the length by three feet. The resultant piece of string clears my waist by much more than six inches. Admittedly, I may be breathing in slightly so as not to look too much like a fatty, and certainly not wanting to be compared to a planet, but the excess of string leads me think I have somehow misunderstood. Could it be that my waist is somehow not adhering to standard laws of mathematics? Should I be concerned and maybe modify my diet? Please help put a simple man out of an ever increasing amount of confusion and worry.

 1242387.  Thu Jul 13, 2017 7:08 pm Dear Worried of Tunbridge Wells, I wouldn't worry about it too much A "well-wisher"

 1242415.  Fri Jul 14, 2017 3:38 am I think the idea is that the string, whatever it is wrapped round, only has to be lengthened by the tiny proportion mentioned, i.e. three feet added to 25,000 miles.

1242421.  Fri Jul 14, 2017 4:40 am

 As If! wrote: I have tried wrapping a piece of string around my waist and then increasing the length by three feet. The resultant piece of string clears my waist by much more than six inches.

Are you sure? You may be breaking the known laws of mathematics.

The circumference of any circle is related to its radius by the formula "2πr".

If "R" is the radius of the earth, the circumference of a piece of string wrapped around it is 2πR. However, if you increase the radius so that the string is now 6 inches above the surface, the radius becomes R + 6", so the formula for the circumference becomes:

2π(R + 6")

Using what's known as the "distributive law", we can expand this equation like so:

2π(R + 6") = 2πR + 2π6"

Now, 2πR is the original length of the piece of string wrapped around the Earth. So, in order to raise it 6 inches above the surface, we only need to increase the length by the 2π6" term. Since π = 3.14159265, we can easily calculate this:

2π6" = 41" = 3'5"

Now, notice that, at no point, have we specified what is the value of "R". I mentioned at the start it is the radius of the Earth but, since we haven't specified a value in the equations, it could be anything. It could the radius of the Sun, or the Milky Way, or your waist. No matter what the string is wrapped around, if we want to raise it 6 inches above the surface, we have to increase its length by 2π6" or 3'5".

We can also go the other way. If we increase the size of the string by 3 feet, what increase in radius do we achieve? This is just doing the sum backwards. We'll call the increase in radius "x", so the equation becomes:

3 feet = 2πx

therefore x = 3 feet / 2π

= 3 feet / 2 * 3.14159265

= 0.47746 feet

= 5.73 inches (12 inches to 1 foot)

= just under 6 inches

I suspect that, when you increase the string around your waist, your measurement of the increase in radius is hampered slightly by the difficulty of keeping the string in an absolutely perfect circle while you measure it.

It's an odd phenomenon. People naturally think that you would need to increase the string around the Earth a lot more, or the string around your waist a lot less, but they're both the same.

As an aside, this counter-intuitive nature of Pi can be used to win bets in pubs. Just bet someone that the circumference of a glass is bigger than the height of the glass. The radius of the mouth of the glass looks small but, given the value of Pi, its circumference will be over 3 times bigger than this.

This bet always works on pint glasses, and even works on surprisingly tall, thin glasses.

1242428.  Fri Jul 14, 2017 5:08 am

 dr.bob wrote: bet someone that the circumference of a glass is bigger than the height of the glass

Now he tells me, when my drinking days are over... :-/

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