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yesudas ramachundra asks

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Post by MaxEntropy_Man Sat Dec 27, 2014 11:59 am

supposing a ship to sail from a given place A, in a given direction AQ, at the same time that a boat from another place B sets out in order (if possible) to come up with her, and supposing the rate at which each vessel progresses to be given Vs (for ship starting at A) and Vb (for boat starting at B) such that Vb < Vs, it is required to find in what direction the latter must proceed, so that if it cannot come up with the former, it may however approach her as near as possible.
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Post by Seva Lamberdar Sat Dec 27, 2014 12:52 pm

It sounds like a problem needing the application of calculus of variations for solution.
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https://docs.google.com/document/d/1bYp0igbxHcmg1G1J-qw0VUBSn7Fu

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Post by MaxEntropy_Man Sat Dec 27, 2014 1:18 pm

the problem is from a book titled, "chases and escapes: the mathematics of pursuit and evasion" buy paul nahin. in the book he refers to this problem which he found in an original book by an obscure indian mathematician, yesudas ramachundra (19th century), full of extrema problems which he solves using ingenious algebraic methods involving no calculus whatsoever. it can however be simply solved using calculus.
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Post by Seva Lamberdar Mon Dec 29, 2014 1:58 pm

Naturally, considering the roots of calculus were in geometry and algebra. Thus any problem which can be solved by using calculus (including the calculus of variations) should also be possible to find its solution, albeit quite tediously, by using geometry and algebra.
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https://docs.google.com/document/d/1bYp0igbxHcmg1G1J-qw0VUBSn7Fu

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