Elizabeth Kolbert' profile of the architect-inventor is a pretty nice overview of the man, his inventions and his quirks. Here's an excerpt from the section where Fuller's geodesic dome makes its first appearance:
Following this string of disappointments, Fuller might have decided that his “experiment” had run its course. Instead, he kept right on going. Turning his attention to mathematics, he concluded that the Cartesian coördinate system had got things all wrong and invented his own system, which he called Synergetic Geometry. Synergetic Geometry was based on sixty-degree (rather than ninety-degree) angles, took the tetrahedron to be the basic building block of the universe, and avoided the use of pi, a number that Fuller found deeply distasteful. By 1948, Fuller’s geometric investigations had led him to the idea of the geodesic dome—essentially, a series of struts that could support a covering skin. That summer, he was invited to teach at Black Mountain College, in North Carolina, where some of the other instructors included Josef Albers, Willem and Elaine de Kooning, John Cage, and Merce Cunningham. (“I remember thinking it’s Bucky Fuller and his magic show,” Cunningham would later recall of Fuller’s arrival.) Toward the end of his stay, Fuller and a team of students assembled a trial dome out of Venetian-blind slats. Immediately upon being completed, the dome sagged and fell in on itself. (Some of the observers referred to it as a “flopahedron.”) Fuller insisted that this outcome had been intentional—he was, he said, trying to determine the critical point at which the dome would collapse—but no one seems to have believed this. The following year, Anne Fuller sold thirty thousand dollars’ worth of I.B.M. stock to finance Bucky’s continuing research, and in 1950 he succeeded in erecting a dome fifty feet in diameter.
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