[atan] provides a handy way to ask Tcl for the value of pi:

 % expr {atan(1) * 4}
 3.1415926535897931

[MGS] Actually, using acos() is (slightly) more efficient:

 % set tcl_precision 17
 17
 % expr {acos(-1)}
 3.1415926535897931

''Does anyone have any data on which method is preferable from a numerical point of view?''

[IDG] Both contain the assumption that the transcendental functions are accurate to the last ulp. In many math libraries this is not so. I think you are safer with a string representation:

 set pi 3.1415926535897931

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[Math function help] - [Arts and Crafts of Tcl-Tk Programming]
- [Category Mathematics]