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Comment on The Planet, some string and a bell.

Since we’re doing strings around the Earth, here’s the simplest, most unintuitive fact in geometry:

Say you have a string wrapped taut around the planet (purely spherical), like a belt. You want to raise that string up so that it’s one meter above ground all the way around the planet. How much more string do you need?

I’ll give you a hint. You don’t need to know the radius of the Earth to know the answer.

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towerful@programming.dev ⁨1⁩ ⁨year⁩ ago
c = pi x d

So, to increase d by 2 meters (cause d = 2 x r), that’s 2 X pi, or 6.28 meters for string?

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- PetDinosaurs@lemmy.world ⁨1⁩ ⁨year⁩ ago
  Correct.
  
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  - davidgro@lemmy.world ⁨1⁩ ⁨year⁩ ago
    To really emphasize it, the same amount of extra string would be needed if it was instead wrapped around a small marble at first and the diameter expanded by the same amount.
    
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- TheActualDevil@lemmy.world ⁨1⁩ ⁨year⁩ ago
  So I’m bad at math. Can you explain why we’ve decided to multiply pi by 2? Is there an articulable reason or is it just a rule?
  
  c+x= pi * (d+2) in this case, right? So where did that multiply pi by 2 come from?
  
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  - reattach@lemmy.world ⁨1⁩ ⁨year⁩ ago
    Distribute the pi on the right side of your equality, and replace c with pi*d:
    
    c+x = pi*(d+2) pid+x = pid + pi2 x = pi2
    
    To generalize for an height h, x = pi2h
    
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    TheActualDevil@lemmy.world ⁨1⁩ ⁨year⁩ ago
    Oh, I see now. I missed some pretty basic math there with that distribution. That makes sense now, thank you!
    
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