It's a small world

Geometry Level pending

According to Wikipedia, the Earth's equatorial circumference is 40075.017 km (24901.461 mi). The meridional (at the poles) circumference, however, is somewhat less at 40007.86 km (24859.73 mi) due to the Earth's rotation. If one assumes its surface to be uniform, what is the maximum distance (to the nearest whole number of kilometers) between any two points on Earth's surface?


The answer is 12756.

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1 solution

John Miller
Jul 8, 2017

Answer: 12756

The shortest distance between any two points is a straight line. The maximum diameter of Earth is 40075.017 km. 40075.017 km divided by pi is 12756.274 km. Thus, the answer to the nearest kilometer in 12756.

The layout of the question, as well as the common manner of thinking about travel between points on the surface of Earth often causes people to immediately assume a curvilinear surface trajectory between points is required when, in fact, a straight line through the sphere of Earth is the correct solution.

Can you clarify what you mean by "the surface is uniform"? There are a lot of "relative ellipsoids" that satisfy the circumferences stated.

Calvin Lin Staff - 3 years, 11 months ago

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