σ has potential, but there's a pretty bad conflict with standard deviation. The circle constant shows up an awful lot in statistics.
Who cares about tau sounding like a "t" for "turn"
Pi comes from perimeter, phi comes from Phidias, etc. There's a long tradition of naming constants using a linguistic root (typically Greek). To my knowledge, there's no precedent for using a symbol based on its visual appearance to a geometric object. (Of course, you could always break with tradition.)
Who cares about tau sounding like a "t" for "turn"
Pi comes from perimeter, phi comes from Phidias, etc. There's a long tradition of naming constants using a linguistic root (typically Greek). To my knowledge, there's no precedent for using a symbol based on its visual appearance to a geometric object. (Of course, you could always break with tradition.)