Stadiums are circular in shape because in a circle the radii / radius is the same . So , whichever side you are sitting , you can enjoy the sport . In football and other team sports , it can be a square or a rectangle . It is because we have people supporting a particular team . So , they sit the opposite side of the opponent .
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They were not, actually, dome shaped. They were amphitheatre semicircles and they were constructed like this to support as better acoustics as possible.