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Scientists have calculated the longest direct land route in the world: 11,241 km


Illustration of Patrick Anderson, in which he suggested the longest possible direct route by sea in 2012

In December 2012, a curious discussion broke out in / r / MapPorn. One of the users under the nickname Kepleronlyknows (Patrick Anderson) published an image with a map of the world, which depicted a direct shipping route. Patrick hypothesized that this is the longest straight route that can be laid on the water on our planet. Without a single turn, you will swim in a straight line about 32,000 kilometers, starting in the Pakistan area and finishing in Kamchatka. Absolutely direct route passes by Africa, South America and across the Pacific Ocean to Russia itself.

Of course, the author did the calculation by intuition. He invited the forum users to test his hypothesis and find a longer route, if one exists. Or try to prove that this particular route is the most direct one.

The message caused a heated debate: hundreds of members of the forum leaned over maps and globes. The main question is whether it is possible to break this record ( UPD: approximately the same debate turned around in the comments to this article on the GT ). Along the way, another question arose: what is the longest route in the world in a straight line over land, and not over the sea? That is, how much you can go in a straight line, never stumbled upon the sea.
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It is clear that the resulting curve must belong to a large circle around the sphere of the globe (for simplicity, we can consider it a sphere). This circle connects points on the surface of the sphere in the shortest possible way. But how to find these circles with the right solution?


The circle that connects the highest and lowest points on the surface of the earth.

Apparently, among the "hotheads" on the Reddit forum, there were still people with a fundamental education who thoroughly approached the problem. So, get acquainted with the scientific work of Rohan Chabukswar from the research center United Technologies (Ireland) and Kushal Mukherjee (Kushal Mukherjee) from the research division of IBM Research in India. These guys have developed a robust algorithm for calculating the longest straight path on land or at sea. The scientific article was published on April 9, 2018 on the site of the preprints arXiv.og ( arXiv: 1804.07389v1 ).

Of course, it immediately comes to mind to solve the problem by brute force - to sort through all possible circles along the terrestrial sphere. But this is too resource-intensive task: on the world map with a resolution of 1.85 km, more than 230 billion such circles will be obtained. Each of them consists of 21,600 individual points, which is a total of more than five trillion points for calculation.

But Chabuksvar and Mukherjee developed a faster method based on an algorithm known as the branch and bound method.

The branch and bound method is a general algorithmic method for finding optimal solutions to various optimization problems, especially discrete and combinatorial optimization. Essentially, the method is a variation of complete enumeration with the screening of subsets of feasible solutions, which obviously do not contain optimal solutions. In fact, instead of evaluating all the solutions, the algorithm checks one branch after another (an analogue of brute force). But another method, called limiting, significantly reduces the brute force area. Each branch contains a subset of potential solutions, one of which is the optimal solution. The trick is to find the property of subsets, which depends on how close the solutions are to the optimal one.

This type of computation required much less computational resources: “The algorithm returned the longest path in about 10 minutes of calculations for the waterway and 45 minutes of calculations for the earthly path on a standard laptop,” say the researchers.

And it turned out that Kepleronlyknows was absolutely right. The longest straight waterway starts in Sonmiani, Baluchistan province, Pakistan, where the missile testing ground is located. The route passes between Africa and Madagascar, and then between Antarctica and Tierra del Fuego in South America - and ends in the Karaginsky region of the Kamchatka region in Russia. The length of the route is 32089 kilometers 700 meters .



The longest journey by land begins near the Jinjiang county in Fujian Province, Quanzhou District (China). It goes through Mongolia Kazakhstan, Russia, and finally reaches Europe to finish near the city of Sagres in Portugal. In general, the route passes through 15 countries and is 11241 kilometers 100 meters - more than 101 degrees around the earth's circumference.



Through which countries passes the world's longest direct land route:


If you are interested, you can accurately calculate through which cities the record route in the world passes. Suddenly, some crazy traveler decides to go strictly in a straight line through all of Asia and Europe. Although, probably, the question needs to be put differently: who will do it first and when?

Source: https://habr.com/ru/post/371485/

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