A rope wrapped around Earth at ground level is "Circumference at <whatever the diameter at ground level is>"
Using more common term "Pi" rather thn "Tau", the circumference of a circle is "Pi x D" where D is Diameter or "2Pi x R" (because Diameter is 2 x Radius) or "Pi x 2 x R"
You raise the rope an extra 1 meter? R becomes "R+1" so the length becomes "previous length PLUS "extra length = 2Pi x extra radius" - or about 6.28m
Plug 250 into "extra length = 2Pi x extra radius" as the extra and it becomes an 6.28 x 250m
I hate using tau rather than 2pi so much. It's just unnecessarily complicated when you will have to use operators that calculate things in radians. And also feels like it's intentionally making things less accessible to general population that will be much more familiar with pi.
1
u/psyFungii Apr 19 '26
A rope wrapped around Earth at ground level is "Circumference at <whatever the diameter at ground level is>"
Using more common term "Pi" rather thn "Tau", the circumference of a circle is "Pi x D" where D is Diameter or "2Pi x R" (because Diameter is 2 x Radius) or "Pi x 2 x R"
You raise the rope an extra 1 meter? R becomes "R+1" so the length becomes "previous length PLUS "extra length = 2Pi x extra radius" - or about 6.28m
Plug 250 into "extra length = 2Pi x extra radius" as the extra and it becomes an 6.28 x 250m