Outside of geometry class, the shortest distance between two points is not always a straight line. Not when the points are, say, Chicago and Hong Kong. Between those cities on a round Earth, the shortest distance happens to be a smooth curve passing not far from the North Pole.
So on this clear, chilly day, a Boeing 747 carrying 255 passengers on United Airlines Flight 895 will become the first craft in history to try out a new air route called Polar 4.
Most passengers who board the flight in Chicago don't realize they are making aeronautical history, even though Capt. Watson W. Tranter's preflight announcement includes some welcoming words for two Russian air traffic experts on board the inaugural flight.
Few passengers pay much attention to the eerie arctic icescape that passes below for hours, gradually giving way to desolate settlements in the permafrost of northern Russia.
But three movies and countless beverage-cart passes later, when the big plane touches down at Hong Kong's new airport on the island of Chek Lap Kok, the route has shaved 53 minutes off the scheduled 16-hour flight time. And the jet has burned about 17,000 pounds less fuel than on the usual route.
The passengers are pleased that the marathon route is trimmed. The Russians -- with the prospect of much-needed cash from fees paid by airlines crossing their airspace -- are happy. And the airline is certainly satisfied: Carrying less fuel will permit the jet to carry more passengers, increasing revenue.
"The Russian controllers' English was excellent," says Tranter, the pilot, as he wheels his bags toward Hong Kong customs. "The flight went very, very well. Real smooth."
After nine years of negotiations, equipment upgrades and language lessons, Russia is gradually opening four new polar routes to speed air travel between the Americas and Asia.
Since the first commercial polar flight in July 1998 -- a Cathay Pacific Airlines flight from New York to Hong Kong -- there have been 43 so-called "demonstration" flights on the routes, including the first flight on Polar 4 several weeks ago.
U.S. and Russian officials expect the polar routes, over thousands of miles of frozen Arctic Ocean and Siberian waste, to enter regular commercial use, probably next year.
It's all a stunning contrast with August 1983, when a Soviet MiG fighter shot down a Korean Airlines passenger jet that had strayed into Russian territory, killing all 269 people aboard and sparking some of the bitterest rhetoric of the Cold War.
"That wasn't me, I assure you," says Viktor Petrovich Mitrofanov, 49, a retired Russian military pilot and one of the two Russian Federal Aviation Authority officials on the debut Polar 4 flight.
"Of course, that was a bitter lesson. A terrible thing. I can give a 100 percent guarantee that won't happen again."
Air routes across the Russian Far East first opened in 1993, two years after the collapse of the Soviet Union. Traffic grew rapidly, and about 4,000 international flights each year now cross Russian territory.
But the more efficient polar routes required the development of new long-haul aircraft -- such as the Boeing 747-400, the Airbus 340 and the McDonnell-Douglas 11 -- and lengthy negotiations involving a half-dozen nations.
There were technical puzzles, too. Scientists were consulted about high winds over the Himalayas and volcanic ash from eruptions on Russia's Kamchatka peninsula.
Would jet fuel congeal in the extreme winter cold above the North Pole? (No.) How could air traffic controllers in the arctic outpost of Tiksi, Russia, communicate with American counterparts in Anchorage, Alaska? (The U.S. Federal Aviation Administration helped the Russian station acquire a satellite phone.)
Understanding why the polar routes are so desirable requires a radical reorientation of flat-Earth thinking.
Standard world maps present a two-dimensional Earth and greatly distort distances. On a wall map, it looks as if a good route from Chicago to Hong Kong would simply head southwest over the Pacific Ocean -- a straight line.
Not so. The shortest line between two points on a sphere, any geometer will tell you, is a segment of what's called a "great circle." That is a circle on the surface of a sphere whose plane passes through the center of the sphere; and from America to Asia, the great circle crosses near the pole.
"Flat maps are very misleading," says Gene Cameron, a United Airlines official who has attended the Russian-American talks on the new routes. "If you went directly west from Chicago to Hong Kong, you'd add an incredible distance."
Punching numbers into the computer in his Chicago office, Cameron calculates that a route from Chicago to Hong Kong that passed through San Francisco and Honolulu would be 8,555 miles long. The great circle route, he says, is 6,780 miles. The Polar 4 route is a little longer, 7,156 miles, because of adjustments for air traffic stations and wind.