./a.out 0.84375 0.843750000000000 0: 0/1 1: 1/1 5: 5/6 2: 11/13 2: 27/32 1/1,3/4,4/5,5/6,11/13,16/19,27/32,

(The last line is the list of all best rational approximations; the formatted block above it is just the list of convergents — look at the examples in the post, and the description above the program. I guess I ought to have printed some text in the output, to make the output more clear and self-contained.)

]]>I can’t make heads or tails out of the notation in the Wikipedia article, so I’m not sure what’s wrong.

]]>Do you have an example where it appears not to work?

]]>A general rule of thumb is that when a factoid appears without context, it is a sign to be cautious. What is the surrounding text around this quote? What does the rest of the alleged work discuss? In what context did the authors come up with it? Are there commentaries on this work? To what use was it put to by later society?

In this particular case, the idea of a battery: nowhere, even in the descriptions of opulence by Bana, Dandin or Magha, or even the fantastical science-fiction of Bhoja, is there anything resembling a battery-operated device.

For example if someone says that the Vedic Shulba sutras contain an approximation of √2, then the surrounding context shows why this is plausible: in the context of discussing various brick-altar constructions, there is a description of how to double the area of a square. And it is still in use. If someone says that Hemachandra etc. described the Fibonacci numbers centuries before, then the context makes it clear: there is a well-established tradition of solving problems of enumeration among the prosodists; the Fibonacci numbers show up naturally as the solution to a well-motivated problem, etc. And the solution is dicussed in commentaries.

In general, the meme of “lost technology” is overstated. Arts and skills and ideas can fade away, but material innovations clearly useful to everyone do not tend to perish.

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