Help finding the greatest distance on a map – February 24, 2023 at 08:20PM

What’s up, everyone?

I’m here after recommendations from geography, cartography and mathematics subreddits, following me posting about a question I’m trying to answer.

Anyways, I need to find what is the greatest distance there is inside my country (Portugal). It is not simply the nothernmost-southernmost or westernmost-easternmost points distance, it is some other distance between two points on the border.

Important: the distance I’m talking about is the arc of a great circle (kind of the analog to a straight line, but on a sphere).

There is a tool to measure distances on google maps, but I can’t determine, with scientific rigor, which are the points from which I should calculate the distance.

One guess is that it is between the easternmost point (41.574831,-6.189158) and somewhere like the point 39.395189,-31.263302. But I guess it could be anywhere else along the borders.

I should highlight that some points like the Monchique Islet (which is the westernmost point), the Savage Islands (small islands, islets and reefs that are the southernmost part of Portugal) and even the islet in the west of the Azores that I suspect it may be one of the points, do not appear before zooming or changing to satellite view or even highlighted as part of Portugal (on google maps, at least).

I was recommended to the GIS community and told to look for someone that can map the points alongside the borders and run some kind of computer magic that would calculate the ones with the greatest distance. I know that this problem is known in math as the “smallest circle problem” and on the wiki page with that name there are two different algorithms to solve it. Other than that, there are probably more tools, algorithms and mathematics to solve it, but I don’t know any.

Can anyone, please, help?