pi-related neatness

[javasaurus]

Suppose you have a string that's about 31.4 meters long (actually 10 pi meters for those who care). Then it can be wrapped tightly around a cylinder with diameter 10 meters. If you add 6.3 meters to the string, you can form the lengthened string into a circle, with the cylinder at the center, and the space between string and cylinder is 1 meter all the way around.

The Earth is about 12,756,000 meters in diameter, or about 40,000,000 meters in circumference. Wrap a string (it'll be approximately 40Mm long) tightly around the Earth. Now make the string 6.3 meters (yes, meters!) longer, as in the previous example. If you form the string into a circle with the earth at its center (like the cylinder before), how much gap do you get between the Earth and the string?

The answer may surprise you!
You get the same gap as with the cylinder, 1 meter, all the way around!

Comments

[acroyear70.livejournal.com]

in the "i know its true, but what does it mean" category, i've never quite understood why the derivative of the area of a circle is the circumference.

d(pi*r^2) = 2*pi*r is mathematically obvious (and, in fact, the 1 meter gap is a side effect of that very relationship, i'm sure, though i'm too rusty to prove it right now).

but still, its always been a mathematical fact and convenience; it never gelled in my head as to exactly *why* it should be that way.

[blueeowyn.livejournal.com]

GEEK!

[skimbells.livejournal.com]

i do so love having friends who revel in geekiness - i feel so much more at home this way :-) (it is meant as a compliment)