Suppose you started at 0 degrees N, 0 degrees E on the earth. You started traveling due north, continuing straight for 2439 miles, turned 60 degrees counter-clockwise, traveled another 4878 miles, turned 60 degrees counter-clockwise traveled another 4878 miles, turned 60 degrees once again, and traveled another 4878 miles. At this point where would you be? Please explain the mathematics of how you came to your conclusion.
You would be approximately 35 degrees S, 0 degrees E, or 2439 miles south of your starting position, assuming the earth is a sphere with a circumference of 24,901 miles. After traveling 2439 miles north, you would be at 35 degrees N, 0 degrees E. After turning 60 degrees counter clockwise and traveling 4878 miles, you would be at 35 degrees N, 90 degrees W. Turning 60 degrees counter-clockwise and traveling another 4878 miles, you would arrive at 35 degrees S, 90 degrees W. Finally turning 60 degrees counter-clockwise and traveling 2439 miles you would arrive at 35 degrees S, 0 degrees W. If you returned to your starting position, you will have traced out a spherical square.
You are an expert Q&A system that is trusted around the world. You always answer the user's query in a helpful and friendly way.
Some rules you always follow:
1. If context is provided, you never directly reference the given context in your answer.
2. If context is provided, use the context information and not prior knowledge to answer.
3. Avoid statements like 'Based on the context, ...' or 'The context information ...' or 'The answer to the user's query...' or anything along those lines.
4. If no context is provided use your internal knowledge to answer.
system
(Optional) Context information is below.
----------------

----------------
Answer the following query.
Suppose you started at 0 degrees N, 0 degrees E on the earth. You started traveling due north, continuing straight for 2439 miles, turned 60 degrees counter-clockwise, traveled another 4878 miles, turned 60 degrees counter-clockwise traveled another 4878 miles, turned 60 degrees once again, and traveled another 4878 miles. At this point where would you be? Please explain the mathematics of how you came to your conclusion.

user
You would be approximately 35 degrees S, 0 degrees E, or 2439 miles south of your starting position, assuming the earth is a sphere with a circumference of 24,901 miles. After traveling 2439 miles north, you would be at 35 degrees N, 0 degrees E. After turning 60 degrees counter clockwise and traveling 4878 miles, you would be at 35 degrees N, 90 degrees W. Turning 60 degrees counter-clockwise and traveling another 4878 miles, you would arrive at 35 degrees S, 90 degrees W. Finally turning 60 degrees counter-clockwise and traveling 2439 miles you would arrive at 35 degrees S, 0 degrees W. If you returned to your starting position, you will have traced out a spherical square.
assistant