In 1986, George Wallenstein led an expedition up K2. Among the gear carried to the summit was equipment to help obtain a more accurate survey of the mountain from a satellite. The preliminary calculations by a the University of Washington astronomer, unnamed in all accounts I've read, indicated that K2 was somewhere between 29,064 and 29,228. Big news, which soon leaked out, and news articles around the world proclaimed K2 the new champeen of the world.
Big problem: the figures were wrong. A simple retraction by the U of W wasn't enough to quell the international uproar. Only an official proclamation would suffice, and Ardite Desio, working on behalf of the Italian Research Council, immediately organized expeditions to measure BOTH mountains with the same yardstick. Climbers and equipment were hastened up both peaks, and in October, 1987, Desio made the announcement that the new satellite tale of the tape showed Everest was 29,078 feet high, and K2 28,238. Many reference books haven't caught up with this yet. The above elevations quoted by Guinness, the World Almanac and AOL's kw: Atlas cite China's 1973 measurements of 29,028 and 28,250 (in meters in AOL's case), and a FAQ at nationalgeographic.com inexplicably gives 29,108 and 28,268. But informed sources now agree that Everest is the top of the world.
http://www.straightdope.com/columns/read/1467/which-is-taller-mt-everest-or-k2
On edit--I thought the graphic at the end of the video was claiming K2 as the tallest mountain. It was my eyes that failed in this case.
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