1
$\begingroup$

I'm reading about how a "straight line" depends on the geometry of space. While I think I understand this, the example people give is:

"Imagine a straight line on earth connecting two cities. It's actually curved because the earth is curved".

My response to that would be "Well no, because a truly straight line would cut through the earth. Like a straight string would cut through an apple".

So question: If two people took an infinitely strong and light string, stood on opposite ends of the earth, and pulled almost infinitely tightly, would the string curve around the earth a few feet above, or would it cut through to the core?

$\endgroup$

closed as unclear what you're asking by Norbert Schuch, user36790, John Duffield, Wolpertinger, heather Sep 9 '16 at 23:55

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 1
    $\begingroup$ Yes it would cut. You're quibbling about the meaning of "straight". Does it mean straight in Euclidean 3-space, or a geodesic on a surface, like the surface of the Earth. Most people don't know the word "geodesic", but that's what they mean. $\endgroup$ – Mike Dunlavey Sep 8 '16 at 17:25
1
$\begingroup$

What this example is trying to point out is that in a 2 dimension space like the surface of a sphere, 'straight' lines are meaningless and the shortest path in this case is called 'geodesic'. If you try to 'pull the rope' and 'cut' the earth' as you mentioned, then you are in a 3d Euclidean space which is not the case in this example.

$\endgroup$
  • $\begingroup$ So the string would indeed cut through the earth, and not curve around it? $\endgroup$ – Bhagwad Jal Park Sep 9 '16 at 15:12
  • $\begingroup$ No, the cutting takes place at center but not at ends. For central parts normal force will get an efficient maximum cut. Strong steel cable and soft earth cut up to some depth like a crescent and no cutting takes place at antipodal points. But yes, if the rope is *full *circumference (40,000 km) and when the two guys are side by side exerting forces in opposite directions it will cut all around as a full circle while shrinking. Try putting a string around a rasgulla, and pulling it.It is assumed we are on great circles. $\endgroup$ – Narasimham Sep 12 '16 at 18:36

Not the answer you're looking for? Browse other questions tagged or ask your own question.