NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
A puzzle
From: Frank Reed
Date: 2008 Jun 05, 10:29 -0400
From: Frank Reed
Date: 2008 Jun 05, 10:29 -0400
Here's a little math puzzle, related to celestial navigation calculations. Suppose I take three angles which have been rounded to the nearest tenth of a minute, and I add them up. What is the error in the sum? Specifically, what is the expectation value of the error? Or if you prefer, what is the standard deviation of the error? I will offer my "guess": the standard deviation of the error is 0.05 minutes of arc (a twentieth of a minute of arc) exactly. Please assume that the angles *before* rounding have no intrinsic error. As an example, I have these angles: 43.681221' 12.066312' 3.625021' I add these numbers up, and get some answer. Now I round them to the nearest tenth of a minute of arc: 43.7' 12.1' 3.6' If I add up these rounded numbers, the sum will differ from the previous one by a small amount. Now I do this sort of calculation a large number of times. What is the standard deviation of the difference between the two sums (exact and rounded)? -FER PS: busy, busy for the next several days. I won't have much time to post... --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---