Group Theory in the Bedroom, and Other Mathematical Diversions by Brian Hayes

Author:Brian Hayes
Language: eng
Format: epub, mobi
Publisher: Farrar, Straus and Giroux
Published: 2008-03-14T16:00:00+00:00

25

3

+2

With this ratio the slower wheel turns in 191.67 minutes, for an error of two-thirds of a minute.

Further approximations are constructed in the same way, always adding the latest entry in the table to whichever of its neighbors reduces the error term. The method is deterministic, with no need for guesswork or trial and error. And, like any good algorithm, it is guaranteed to terminate eventually. The end comes when the process converges on the original ratio , which necessarily has an error of zero. For Brocot’s example, the final table looks like this:

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.