Dear Roger, Thank you for pointing the list at this YouTube video
http://www.youtube.com/watch?v=cFH1lz0212o I found that very compelling and, indeed, all the associated 10-minute clips. I particularly noted Al-Battani's expression for the radius of the Earth: R = h.cos(phi)/(1-cos(phi)) where h = height of some mountain phi = dip to the horizon from the summit With John Carmichael in mind, I comment that this is the kind of thing that 14-year olds could derive in the 1950s but Mathematics graduates have to struggle over today :-)) The value of phi in the clip was about 0.5 degrees and the cosine of 0.5 is 0.99996 or so close to 1 that you need 6-figure tables to make progress (or knowledge of the series expansion for the cosine function, or you could rearrange the expression). I know very little about the history of mathematical tables. There was something in one of the clips about the Arabs developing tables of sin and cos but Al-Battini would need high precision to make use of the quoted expression. The whole procedure seems terribly sensitive to errors in the measurements to me and if it is true that Al-Battini determined the radius of the Earth to 0.1% this way he was very lucky as well as very clever!! Thank you also for reminding the list about God's Longitude and Simon Cassidy's work. It is one of God's better jokes that He should have drawn His Longitude through Washington!!! Best wishes Frank --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
