28 Jan 18
Originally posted by @handyandyAn infinite number in fact!
Name a place on Earth's surface where you can travel one mile due south, then
one mile due west, then one mile due north, and end up exactly where you started.
The traditional answer is the North Pole, but can you find at least one other spot?
28 Jan 18
Originally posted by @wolfgang59Perhaps, but I'll settle for one.
An infinite number in fact!
(I hope this isn't another time zone fiasco.)
28 Jan 18
Originally posted by @handyandyAnywhere on a line of latitude 1 mile north of a line of latitude
Perhaps, but I'll settle for one.
(I hope this isn't another time zone fiasco.)
which is 1 mile around the South pole. (Or half, or quarter or eighth ...)
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28 Jan 18
Originally posted by @handyandyBognor Regis.
Name a place on Earth's surface where you can travel one mile due south, then
one mile due west, then one mile due north, and end up exactly where you started.
The traditional answer is the North Pole, but can you find at least one other spot?
(There's no known escape from Bognor Regis).
28 Jan 18
Originally posted by @wolfgang59Correct! That second line of latitude, one mile around the South Pole: How far is it from the pole?
Anywhere on a line of latitude 1 mile north of a line of latitude
which is 1 mile around the South pole. (Or half, or quarter or eighth ...)
28 Jan 18
2 edits
Originally posted by @handyandyIf you began traveling due south at a point less than one mile from the south pole, wouldn't you at some point (along that line) be traveling north before traveling west?
Correct! That second line of latitude, one mile around the South Pole: How far is it from the pole?
edit: okay, I get it now. After traveling due south for one mile you arrive at a point where, after traveling west and completing a full circle, the length of that circle will equal one mile.
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29 Jan 18
1 edit
Originally posted by @handyandyDo you mean what latitude? If so, then its latitude
Correct! That second line of latitude, one mile around the South Pole: How far is it from the pole?
(90 - 1/R*180 / π ) or approximately 89.986 degrees.
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Originally posted by @lemon-lime"edit: okay, I get it now. After traveling due south for one mile you arrive at a point where, after traveling west and completing a full circle, the length of that circle will equal one mile."
If you began traveling due south at a point less than one mile from the south pole, wouldn't you at some point (along that line) be traveling north before traveling west?
edit: okay, I get it now. After traveling due south for one mile you arrive at a point where, after traveling west and completing a full circle, the length of that circle will equal one mile.
No, what your saying is impossible on Earth (but you probably wouldn't know that without doing the math).
All the longitudinal great circles intersect at the pole. From the pole you travel South 1 mile. Then you may travel ANY distance you like due West. Then travel 1 mile due North and you will be back at the pole due to the intersection of the great circles.
29 Jan 18
3 edits
Originally posted by @joe-shmoHow are you able to travel south from the South Pole?
"edit: okay, I get it now. After traveling due south for one mile you arrive at a point where, after traveling west and completing a full circle, the length of that circle will equal one mile."
No, what your saying is impossible on Earth (but you probably wouldn't know that without doing the math).
All the longitudinal great circles intersect at the ...[text shortened]... 1 mile due North and you will be back at the pole due to the intersection of the great circles.
The question in the OP is where else (other than the North Pole) can you travel south for one mile, then west for one mile, then north one mile and end up where you started. If you find a latitudinal line near the south pole exactly one mile long, bringing you back to where you started your westward journey, then travel one mile north from that point, then any point along that slightly higher latitudinal line can be your starting point.
29 Jan 18
Originally posted by @handyandyThat second line of latitude, one mile around the South Pole: How far is it from the pole?
Correct! That second line of latitude, one mile around the South Pole: How far is it from the pole?
A stones throw...
29 Jan 18
Originally posted by @joe-shmo?
"edit: okay, I get it now. After traveling due south for one mile you arrive at a point where, after traveling west and completing a full circle, the length of that circle will equal one mile."
No, what your saying is impossible on Earth (but you probably wouldn't know that without doing the math).
What makes you think that?
29 Jan 18
Originally posted by @wolfgang59Imagine a circle that is centered at the South Pole with a circumference of exactly one mile.
Anywhere on a line of latitude 1 mile north of a line of latitude
which is 1 mile around the South pole. (Or half, or quarter or eighth ...)
The edge of this circle would be about 0.159 miles (roughly 280 yards) from the pole. Any
point one mile north of this circle (approximately 1.159 miles north of the pole) will satisfy
the conditions of the puzzle.
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29 Jan 18
2 edits
Originally posted by @wolfgang59My mistake.
?
What makes you think that?
Until I saw the post from Handy Andy I was actually missing the solution. 😵 So just applying it to starting at the north pole solution. Walking a mile due south, and saying it would not be possible to complete a full circle due west that was 1 mile on the Earth beginning at a pole.
"Imagine a circle that is centered at the South Pole with a circumference of exactly one mile. The edge of this circle would be about 0.159 miles (roughly 280 yards) from the pole. Any point one mile north of this circle (approximately 1.159 miles north of the pole) will satisfy the conditions of the puzzle."
Again, my misunderstanding.Sorry