# Question - What distance

• luiseduardo
In summary, the conversation discusses different scenarios of continuously walking in different directions and where the traveler would end up. It is noted that in all cases, the traveler will end up at the starting point, except for walking north or south where they would reach a pole. The question of whether the traveler is following a map, compass, or a great-arc is also raised, with the possibility of spiraling towards the South Pole depending on the starting point and direction of travel.

#### luiseduardo

Hello all,

I am a student of high school and found an interesting question, but I do not know resolve. I'm from Brazil, sorry for the mistakes in English.

I believe that to understand one must understand the question before, so I'll have to post the two here:

2) Where a traveler will come if he keeps always walking to:

a) North
b) South
c) east
d) West

3) Where it will come if you keep walking in a southwesterly direction? How many miles he has walked to the end point? How many rounds he will have made around this point?

In all the 4 cases one ends up at the starting point.

grzz said:
In all the 4 cases one ends up at the starting point.

Not quite. If he keeps walking north or south he will end up at a pole. If he keeps walking in the same direction, his direction name is reversed (S to N or N to S).

Going southwest will have a similar problem. At some point he is as far south as possible, so continuing in the same direction is now northwest.

Mathman is correct.

A question of the question...

Are we walking southwest, following
1. the map
2. the compass, or
3. a great-arc

I'm thinking we would spiral to the South Pole, with a different spiral for each of the above. We would end in ever decreasing spiral around the south pole, except for using the compass.. then we would end up in an ever decreasing spiral around the south magnetic pole.

Soutwest geographically not magnetically.

Following a great arc is almost the most interesting. If you start out walking Due East from Fairbanks, AK, following a great arc, you'll pass very near to Omaha, NE.

But you need to specify a starting point to get really picture what each means. If you walk due East or West, you wind up back at your starting point regardless of what type of motion you actually mean.