Different Latitude and Longitude on Same Meridian

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Problem

There are $3$ remarkable places on the globe that differ in latitude,
as well as in longitude;
and yet, all of them lie under the same meridian.


Solution

Let one point be one of the poles.

This has a latitude of $90 \degrees$, either north or south.

Let another point be a number of degrees of latitude different from $90 \degrees$.

Let a third point be a different number of degrees of latitude, again different from $90 \degrees$, $180 \degrees$ of longitude different from the second point.

All $3$ points have a different latitudes by construction.

The pole has no defined longitude.

Hence all $3$ points have different longitude.

But all $3$ points are on the same great circle of Earth.

Hence, using the definition of meridian to mean that complete great circle, the puzzle is seen to have this solution.

It is of course to be noted that, apart from the pole, the points can be chosen arbitrarily to suit the conditions.

$\blacksquare$


Sources

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