I just realized that the Roman Pantheon may have been designed as a illustration of Archimedes's "Hat Box Theorem". From the inside of the Pantheon, the top half is a hemisphere and the bottom half is a cylinder of the same height as the radius; i.e., the continuation of the sphere that just fit inside the dome would have just touched the floor in the middle. Hadrian is known to have been 1) fond of everything Greek; 2) an amateur architect; and 3) fond of domes. He certainly wasn't good enough to design the Pantheon, but he certainly would have appreciated the architect who proposed it to him. http://en.wikipedia.org/wiki/Pantheon,_Rome "The height to the oculus and the diameter of the interior circle are the same, 43.3 metres (142 ft), so the whole interior would fit exactly within a cube (also, the interior could house a sphere 43.3 metres (142 ft) in diameter).[33] These dimensions make more sense when expressed in ancient Roman units of measurement: The dome spans 150 Roman feet; the oculus is 30 Roman feet in diameter; the doorway is 40 Roman feet high." http://mathworld.wolfram.com/ArchimedesHat-BoxTheorem.html