Ellipsoid distance on Earth

A funny example of this in practice happened a few years ago during the United Airlines and Continental Airlines merger.

When they switched computer systems, somehow they switched the method they used to calculate the distances between cities for their frequent flyer program. Before the merger, both companies used the ellipsoid method. During the computer systems cutover, the method suddenly changed to a spherical approximation. They also used an incorrect

The difference resulted in shorting flyers of a few (I think the most I saw was 40) frequent flyer miles per leg. They got caught within a couple days and 'fixed' the 'accidental' change. One of those things they seemed to hope no individual would catch but that over many many flyers would add up to a significant cost savings.

The alternatives are either using the pythagoras algorithm, which only makes sense for short distances (unless you are a flat earth believer) or the haversine algorithm: https://en.wikipedia.org/wiki/Haversine_formula. Haversine is fine unless you really need super accurate results. The shorter the distance the less of an issue this is.

If you are doing simple distance searches on a map with small radiuses, use whatever is good enough. I've used pythagoras for this in the past as part of a ranking formula as it is a lot cheaper to do that and it does not have to be super accurate.

Why does this use all the mathematical function from scipy instead of the built-in math? Are there significant benefits to that?

For a lot of use cases, the error in using the spherical approximation is small enough that it doesn’t matter. For instance, measuring distance between two points in the same city, you can happily use the shorter function and not worry about it.

This is an easy-to-implement approach, with a great explanation.