If you wrapped a string around the earth at the equator and pulled it tight, and then added one foot to the length of the string, what would be the uniform gap formed between the string and the surface of the earth? Surprising answer!
Your avatar reminded me of this: Kekulé had another dream, in which he saw atoms dance around, then form themselves into strings, moving about in a snake-like fashion. This vision continued until the snake of atoms formed itself into an image of a snake eating its own tail. This dream gave Kekulé the idea of the cyclic structure of benzene.
I'd say the circumference =2 * pi * r So, r = c/(2*pi) The new radius is r' = (c+1 foot)/(2*pi) So, the difference in radius (the height above earth) is the difference in r which is r'-r, which is (c+1 foot)/(2*pi) -c/(2*pi) = ((c+1) - c) / (2*pi) =1/(2pi) True?
1 foot divided by 2*pi equals 12 inches divided by 6.28 which rounds up to 2 inches, which is what I said above, so well done.
It's so obvious, there's no need..... and then you need people to be able to understand it...... that makes 2 of us.....
Yes. So it doesn't matter how long the string is or how large the object. By adding one foot, the gap will always be 1/2pi, be it a soccer ball or a planet. That is sooooooooooo counter intuitive!
True, but we have the luxury of knowing stuff like pi, which I think came from wrapping strings around stuff and making more and more accurate measurements. I'm always blown away by how much progress has been made through thought experiments like Einstein's and measurement of results like the scatter patterns from collisions in particle accelerators.
Pi is a value we discovered, not derived. Likewise, all physical constants can only be determined using measurements. You don't do physics without math. In fact you really can't even start a physics problem [real physics] without knowing Calculus. The Greeks taught us that philosophy [no math] has limited value. The world cannot be understood through thought experiments. If Einstein couldn't do the math, he would just be another nameless dreamer long forgotten, who never accomplished anything.
True. Not good. I was going to make it clearer that for every foot of string added the radius increases by 1 foot /2pi. But, it was starting to look like I was already overly pedantic.
Well, I certainly agree that if someone plans on a college degree in physics they better start cranking on math. In fact, those with physics degrees tend to be very good at applied math. They often get jobs in fields that have everything to do with advanced applied math methods and little to do with physics! On the other hand, there are lots of cool methods for allowing middle school or high school students to derive equations related to gravity, mass, elasticity, etc., without knowing what calculus is. Typically speaking, relationships in physics are understood through measurement. And, Einstein trashed a major percent of physics based on his thought experiments.