Hi Tony, I am pleased to hear that you are thinking of travelling to Beijing. Carpe Diem!
I calculate the number of frequent flier points you will earn as 4904 miles each way. This is based on the equation for Great Circle Distance: Cos(GCD)= Sin(Lat1)x Sin(Lat2) + Cos(Lat1) x Cos(Lat2) x Cos(Long1-Long2) This returns an answer in degrees. Multiply by 69.0468 for statute miles. You will recognize that the equation is the same form, the cosine rule for spherical triangles, as the familiar equation for altitude. I saw the instruments of the ancient observatory during an early morning walk in Beijing in 1992. Unfortunately the observatory didn't open until after we had left for the airport. I was tempted to scale the wall for a closer look but decided the risks of falling or being arrested were too great. There are some useful websites showing the instruments. I was led to these with the link that Claude Hartman mentioned last week. http://www.math.nus.edu.sg/aslaksen/teaching/heavenly.html Follow the links to ancient instruments and scrolling down to the Armillary spheres of Guo Shoujing at the Purple Mountain Observatory at Nanjing. The site, http://vm.nthu.edu.tw/science/astra/ is in Chinese/Martian. Just click on the links on the right to see the pictures of the instruments. It is interesting to note that these instruments were built 350 years before the Jesuits arrived in Beijing. At this time the Chinese were way ahead of Western Europe which was just waking up after the dark ages. These instruments show that the Chinese knew astronomy and celestial navigation. On your flight over read the recent book "1421: The Year the Chinese Discovered the World" by Gavin Menzies. See www.1421.tv This account of the voyages of the Chinese treasure ships is a great made-for-tv book. He weaves quite a story from odd bits of knowledge and old relics. Although many of his claims are outrageous, unsubstantiated and erroneous, he makes the point that the Chinese were the center of world civilization at that time, and then collapsed inward from the costs of expansion. Can history teach us something here. OK, I concede that your countryman, John Holywood (or Johan Sacrobosco) of Yorkshire wrote "De Sphera" in 1220, bringing Ptolemy's advice on how to construct an armillary sphere to the Western Europe. Cheers, Roger Bailey Walking Shadow Designs N48.6 W 123.4 which is 4516 great circle miles from Bedlington -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of tony moss Sent: February 4, 2004 3:03 PM To: Sundial Mail List Subject: Latitude and Linear distances. Fellow Shadow Watchers, I'm so glad that I asked what seemed to be simple question about latitude and linear distances because I have learned so much from the erudite responses - although I must confess that some of them leave me feeling well out of my depth. As I recall it the TV graphic which gave rise to my query was, at best, an oversimplification if not entirely erroneous so honour is satisfied. On the debit side my personal concept of 'Latitude' has required a quick overhaul in the light of the diagrams kindly supplied by Bill Gottesman and Rudolf Hooijenga. My personal conceptualisation is mainly 'graphical' rather than 'numerical' so these did the trick for me. As an added bonus my casual comment about the Chinese astronomical instruments, clearly identified in Roger Bailey's posting, has inspired me with the best possible reason for planning a visit to Beijing at some time in the future. Many thanks to everyone who responded. Tony Moss - -
