Geiger was born in Philadelphia, Pennsylvania, received a bachelor's degree from Drexel University, master's degree from the University of Wisconsin–Madison and PhD in engineering from Columbia University.
While an adjunct professor at Columbia University, Geiger designed the enclosure for the United States pavilion at Expo 70 in Osaka, Japan. He had been tapped after the architecture firm Davis Brody won the design contest for the building. Davis Brody's winning design was a 30-story high air filled "pumpkin" atop the pavilion and they needed an engineer with the expertise to implement it. Geiger was designing the US Pavilion to be capable of withstanding Japan's earthquakes and typhoons when Congress approved only half of the expected budget. To accommodate the new budget, he drastically cut the proposed height and used a low profile cable-restrained air-supported roof, employing a super-elliptical perimeter compression ring and diagonally-run pattern of cables which prevented fabric sag around the perimeter. Geiger's fabric air-supported roof invention was significantly cheaper than the largest fixed dome structure of the day: the Astrodome.
He then joined with engineer Horst Berger to form Geiger Berger Associates and they went on to produce designs for a series of low-cost air-supported structures including the first tensegrity type dome for the Olympic Gymnastics Venue, Seoul, Korea (which had been inspired by the work of R. Buckminster Fuller), first translucent insulated fabric roof at Lindsay Park Sports Centre, Calgary, Alberta, Canada, first “permanent” low profile air-supported fabric roof to cover a stadium at the Silverdome in Pontiac, Michigan.
The partnership with Berger dissolved in 1983 and Geiger formed Geiger Associates, which was acquired by KKBNA in 1986. In 1988, Geiger in partnership with former colleagues from Geiger Associates went on to found Geiger Engineers.
Geiger died in 1989 while traveling in Seoul where he had designed three venues for the 1988 Olympics.
- Silverdome, Pontiac, Michigan (1975)
- Stephen C. O'Connell Center (1980)
- Hubert H. Humphrey Metrodome, Minneapolis, Minnesota (1982)
- BC Place, Vancouver, British Columbia, Canada (1983)
- Lindsay Park Sports Centre, Calgary, Alberta (1983)
- RCA Dome, Indianapolis, Indiana (1984)
- Tokyo Dome, Tokyo (1988)
- Redbird Arena (1988)
- 1988 Summer Olympics venues in Seoul, Korea
- Tropicana Field (1989)
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