NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: First sine table (Ptolemy)
From: Lu Abel
Date: 2009 Jan 21, 22:17 -0800
From: Lu Abel
Date: 2009 Jan 21, 22:17 -0800
I, too, would love to hear how ancient tables were created. Most of us who have taken a college-level math course or looked through various handbooks have seen the infinite series for sines, cosines, and other functions. But two things I remember from having taken a graduate-level course in numerical analysis, especially as might be used on computers: 1. Truncating an infinite series can produce unexpected results. Most famous of these is the Gibbs Phenomenon, where the Fourier transform for a square wave (an infinite series of sine waves which should sum up to the square wave) in fact produces a square wave with large "ears" if the series is truncated. See http://en.wikipedia.org/wiki/Gibbs_phenomenon 2. Numerical algorithms for approximating functions through a finite series often use coefficients different from those in the infinite series to produce more accurate results. James N Wilson wrote: > Were infinite series used in the initial creation of tables? I find in my > ancient college handbook listings of series for just about everything, > including the trigonometric functions. > > Jim Wilson > ____________________________________________________________ > Click here for free information on how to reduce your debt by filing for bankruptcy. > > > > --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---