Very Wrong Math
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Very Wrong Math
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Re: Very Wrong Math
#2Related Wikipedia article: https://en.wikipedia.org/wiki/String_girdling_Earth#Implicat....
The takeaway is that the extra length of the arc is likely much smaller than one would intuitively expect. The problem is usually framed like so: If you wrapped a rope around the earth, how much more rope would you need to add so that it would be 1 meter above the ground at all points? The answer is only 2π meters!
Re: Very Wrong Math
#3Related Wikipedia article: https://en.wikipedia.org/wiki/String_girdling_Earth#Implicat... . The takeaway is that the extra length of the arc is likely much smaller than one would intuitively expect. The problem is usually framed like so: If you wrapped a rope around the earth, how much more rope would you need to add so that it would be 1 meter above the ground at all points? The answer is only 2π meters!
(2pi * (n + 1)) - (2pi * n)
-> 2pi * (n + 1 - n)
-> 2pi * 1
-> 2pi
If I remember my algebra correctly. Someone else check my work I'm a dropout
Re: Very Wrong Math
#4Related Wikipedia article: https://en.wikipedia.org/wiki/String_girdling_Earth#Implicat... . The takeaway is that the extra length of the arc is likely much smaller than one would intuitively expect. The problem is usually framed like so: If you wrapped a rope around the earth, how much more rope would you need to add so that it would be 1 meter above the ground at all points? The answer is only 2π meters!
The only issue I see with this is that as a classic physics trope, we've approximated the earth as a sphere.
If, instead we approximate it as a fractal... then the distance is infinite, or at least highly dependent on the thickness of the rope!
The error in the original is assuming that the radius is proportional to the height above the earth (Earthradius=0?).
Re: Very Wrong Math
#5Related Wikipedia article: https://en.wikipedia.org/wiki/String_girdling_Earth#Implicat... . The takeaway is that the extra length of the arc is likely much smaller than one would intuitively expect. The problem is usually framed like so: If you wrapped a rope around the earth, how much more rope would you need to add so that it would be 1 meter above the ground at all points? The answer is only 2π meters!
The only issue I see with this is that as a classic physics trope, we've approximated the earth as a sphere. If, instead we approximate it as a fractal... then the distance is infinite, or at least highly dependent on the thickness of the rope! The error in the original is assuming that the radius is proportional to the height above the earth (Earthradius=0?).
> infinite, or at least highly dependent on the thickness of the rope
The latter. But that's only if it's not somewhat taut. Some tension brings it closer to a circle and makes the actual thickness pretty unimportant.
But I like the idea overall. It means that lifting up the string makes it smoother and it actually needs less length. How's that for being unintuitive?
Re: Very Wrong Math
#6Earlier quoted context omitted.
The only issue I see with this is that as a classic physics trope, we've approximated the earth as a sphere. If, instead we approximate it as a fractal... then the distance is infinite, or at least highly dependent on the thickness of the rope! The error in the original is assuming that the radius is proportional to the height above the earth (Earthradius=0?).
> infinite, or at least highly dependent on the thickness of the rope The latter. But that's only if it's not somewhat taut. Some tension brings it closer to a circle and makes the actual thickness pretty unimportant. But I like the idea overall. It means that lifting up the string makes it smoother and it actually needs less length. How's that for being unintuitive?
Exactly, if you're only 1cm off the surface you follow every nook and cranny. If you're 10km off the surface only Everest is a blip.
Re: Very Wrong Math
#7Related Wikipedia article: https://en.wikipedia.org/wiki/String_girdling_Earth#Implicat... . The takeaway is that the extra length of the arc is likely much smaller than one would intuitively expect. The problem is usually framed like so: If you wrapped a rope around the earth, how much more rope would you need to add so that it would be 1 meter above the ground at all points? The answer is only 2π meters!
(2pi * (n + 1)) - (2pi * n) -> 2pi * (n + 1 - n) -> 2pi * 1 -> 2pi If I remember my algebra correctly. Someone else check my work I'm a dropout
For convenience, we set τ=2pi. :-)
x = τ(r+1) - τr = τ(r+1-r) = τ(1) = τ
Re: Very Wrong Math
#8Are we talking spacetime?
Re: Very Wrong Math
#9Curious, does the air being thinner affect flight time?
Re: Very Wrong Math
#10Curious, does the air being thinner affect flight time?
I think in a way that’s why planes fly so much further up than you’d think they’d need to. They want more consistent and minimal atmospheric conditions. Less air means less energy means less turbulence, I think?
If you’re talking about friction… oooh that’s an interesting one. Intuitively yes. But is it also negligible?