Where Are You?

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?

Originally posted by @handyandy
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?

An infinite number in fact!

Originally posted by @wolfgang59
An infinite number in fact!

Perhaps, but I'll settle for one.

(I hope this isn't another time zone fiasco.)

Originally posted by @handyandy
Perhaps, but I'll settle for one.

(I hope this isn't another time zone fiasco.)

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 ...)

Originally posted by @handyandy
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?

Bognor Regis.

(There's no known escape from Bognor Regis).

Originally posted by @wolfgang59
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 ...)

Correct! That second line of latitude, one mile around the South Pole: How far is it from the pole?

Originally posted by @handyandy
Correct! That second line of latitude, one mile around the South Pole: How far is it from the pole?

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.

Originally posted by @handyandy
Correct! That second line of latitude, one mile around the South Pole: How far is it from the pole?

Do you mean what latitude? If so, then its latitude

(90 - 1/R*180 / π ) or approximately 89.986 degrees.

Originally posted by @lemon-lime
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.

"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.

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).

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.

How are you able to travel south from the South Pole?

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.

Originally posted by @handyandy
Correct! That second line of latitude, one mile around the South Pole: How far is it from the pole?

That second line of latitude, one mile around the South Pole: How far is it from the pole?

A stones throw...

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?

Originally posted by @wolfgang59
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 ...)

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.

Originally posted by @wolfgang59
?
What makes you think that?

My mistake.

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