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Re: spherical geometry

Last year my wife and I visited Australia. Being thrifty types, we
found the cheapest way to get there. We flew from Vancouver via Air
Canada (to Los Angeles) and Malaysia Airlines, spending a day in Kuala
Lumpur on route to Adelaide. (Yes, Kuala Lumpur is three time zones
west of Adelaide, but the ticket was cheap!)

The flight was quite pleasant, with TV screens at every seat. One
channel on the TV was devoted to a navigation data screen that gave
interesting data like ground speed, a plot of the route, outside air
temperature, and lots of other data in both SI and British Imperial
units. One screen on this channel was a graphic showing the direction
and distance to Mecca relative to our flight path. (The upper deck of
this 747 was a prayer room.)

We don't travel often, and I had never seen this navigation screen
before. I thought to myself: "What a nice piece of software these
muslims had written to facilitate fulfilling their religious
obligations." I retained this illusion until, on the Los Angeles to
Vancouver leg of our return flight, I saw the same software on a brand
new Airbus 300 that showed the directions and distances from LAX to
Beverly Hills and Malibu as we took off! I recall again thinking to
myself "I wonder what sort of prayer is appropriate when one is
oriented toward one of these places!"

Since the return trip (Sydney-Melbourne-Kuala Lumpur-Taipei-Los
Angeles-Vancouver) with no tourist stops en route took 42 hours, I
attribute this particular fantasy to fatigue. One other interesting
result was seen on the navigation screen. On our flight back over the
Pacific our ground speed exceeded sound speed. We reached almost 750
miles per hour! I had not known that the jet stream effect could be so