The fan shape for performance venues is an adaptation of the shoebox. The form mimics the diffusion path of sound waves and reduces the echo effects that occur in more rectangular arrangements. Despite backing of acoustic theory, many people favor the characteristic reverb of a shoebox over the sometimes stale sounding fan configurations.
To better understand how sound travels through a space it is useful to try Ecotect's acoustic ray animations. The animations show how the sound moves with color-coded rays that indicate direct reflecting surfaces, useful sound, masked sound, echoes, border, and reverberation. Unfortunately, I cannot capture these rays in a screen shot. The animation is very useful for analyzing the material and forms of direct reflecting surfaces (particularly at the back of the stage) for their acoustical properties.
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