This is an amazing application of geodesics and vector functions: finding the shortest underwater path.

http://web.mit.edu/newsoffice/2012/underwater-swarms-robots-0308.html

Robotic crafts that sweep the ocean depths in order to map the sea floor, root out pollution, or search for sunken treasure frequently need to answer the question “What is the best way to get from point A to point B?”

Finding the best path could mean many different things: shortest in distance, shortest in time, shortest in energy used. And it can be a tough problem even under the best of circumstances, much less when strong and variable ocean currents are concerned!

But this team of mathematicians, engineers, and ocean scientists at MIT have done it. Not only have they come up with a good algorithm for finding optimal paths for single crafts, but their methods also solve the problem for **formations** of crafts!

Another astonishing application of mathematics.

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