Pete posted this from a non-subscribed address:
Date: Fri, 1 Dec 2006 21:31:14 -0800 From: Peter Salzman <[EMAIL PROTECTED]> Subject: [OT] How do calculators work? To: [email protected] I've always heard that calculators use truncated Taylor series to approximate functions like trig and exp functions. Yet that can't be the whole story: Taylor approximations require more and more terms for convergence as you evaluate the series farther and farther away from the point of expansion. Second, we get into problems with singularities and the radius of convergence. The series converges on a complex disk (or a real interval) that contains no singularities. That presents a major obstacle for calculating logarithms. That's why you always expand log(x + k), rather than log(x). So saying that calculators use power series approximations can't be the whole story. It's a good zeroth order approxmation to the truth. What's the first order correction to the truth? Thanks! Pete ----- End forwarded message ----- _______________________________________________ vox-tech mailing list [email protected] http://lists.lugod.org/mailman/listinfo/vox-tech
