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The Longest Straight Path You Could Travel On Water Without Hitting Land (gizmodo.com)
An anonymous reader quotes a report from Gizmodo: Back in 2012, a Reddit user posted a map claiming to show the longest straight line that could be traversed across the ocean without hitting land. Intrigued, a pair of computer scientists have developed an algorithm that corroborates the route, while also demonstrating the longest straight line that can be taken on land. The researchers, Rohan Chabukswar from United Technologies Research Center Ireland, and Kushal Mukherjee from IBM Research India, created the algorithm in response to a map posted by reddit user user kepleronlyknows, who goes by Patrick Anderson in real life. His map showed a long, 20,000 mile route extending from Pakistan through the southern tips of Africa and South America and finally ending in an epic trans-Pacific journey to Siberia. On a traditional 2D map, the path looks nothing like a straight line; but remember, the Earth is a sphere.
Anderson didn't provide any evidence for the map, or an explanation for how the route was calculated. In light of this, Chabukswar and Mukherjee embarked upon a project to figure out if the straight line route was indeed the longest, and to see if it was possible for a computer algorithm to solve the problem, both for straight line passages on water without hitting land or an ice sheet, and for a continuous straight line passage on land without hitting a major body of water. Their ensuing analysis was posted to the pre-print arXiv server earlier this month, and has yet to go through peer review. "There would be 233,280,000 great circles to consider to find the global optimum, and each great circle would have 21,600 individual points to process -- a staggering 5,038,848,000,000 points to verify," the researchers wrote in their study.
Anderson didn't provide any evidence for the map, or an explanation for how the route was calculated. In light of this, Chabukswar and Mukherjee embarked upon a project to figure out if the straight line route was indeed the longest, and to see if it was possible for a computer algorithm to solve the problem, both for straight line passages on water without hitting land or an ice sheet, and for a continuous straight line passage on land without hitting a major body of water. Their ensuing analysis was posted to the pre-print arXiv server earlier this month, and has yet to go through peer review. "There would be 233,280,000 great circles to consider to find the global optimum, and each great circle would have 21,600 individual points to process -- a staggering 5,038,848,000,000 points to verify," the researchers wrote in their study.
curvature of the Earth
Huh? If you look at TFA, the line clearly has an endpoint on the western edge of the Indian subcontinent, and does not approach western Europe at all..
5,038,848,000,000 points is nothing on a modest PC (eg. An i7 with 8 cores at 3GHz is 24,000,000,000 clock cycles per second).
I can't imagine it took more than a few minutes to run.
I know this is Slashdot and we don't read the article... but the article has this to say about the subject:
"Armed with this technique and a regular laptop computer, Chabukswar and Mukherjee calculated the sea route in just 10 minutes."
In spherical geometry:
That last one is the rule you've come across.
I don't think these researchers dug deep enough into the history of this. For those who are interested, here is the reddit post:
https://www.reddit.com/r/MapPorn/comments/15mwai/the_longest_straight_line_you_can_sail_almost/
Here's another reddit thread that he cross-posted to from five years ago; it seems that the researchers didn't dig deep enough:
https://www.reddit.com/r/todayilearned/comments/15mxxp/til_you_can_sail_almost_20000_miles_in_a_straight/
Apparently he learnt it from a Wikipedia article, where it is also reported (without citation) that the longest distance only on land is 13,573 km (8,434 mi).
The edit was added with this revision by Wikipedia user Muh1974 (who doesn't have a Wikipedia user page). The Talk page around that time has unreferenced "I remember reading somewhere" speculation about the longest great circle. My guess is that Muh1974 checked (somehow) that this path was valid, and had a distance at least comparable to the other ones mentioned in the wikipedia article, but that's where the trail goes cold for me.
Ask me about repetitive DNA