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I'm an avid tauist (tauday.com) and I don't like the fact that Mathematica displays equations with $\pi$ instead of $\tau=2\pi$. I know that I can "force" it to display $\tau$ by e.g. Sum[ArcTan[1/n^2],{n,1,Infinity}] /. [Pi] -> [Tau]/2 (with backslashes) but writing "/. [Pi] -> [Tau]/2" (with backslashes) at the end of everything is very annoying.

Is there a command which would have the effect of applying "replace every $\pi$ with $\tau/2$" to a whole notebook so that I can write it just once and then never again?

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Use $Post.

$Post = (# /. π -> τ/2) &;
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    $\begingroup$ You will need a few more things such as Unprotect[\[Tau]]; N[\[Tau], prec : _ : MachinePrecision] := N[2 Pi, prec]; SetAttributes[\[Tau], {Constant, Protected}]; (*Protect[\[Tau]];*) $\endgroup$
    – Bob Hanlon
    Commented Mar 28, 2023 at 17:47
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    $\begingroup$ @BobHanlon What exactly does that accomplish $\endgroup$
    – Vestoo
    Commented Mar 28, 2023 at 18:52
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    $\begingroup$ Once you have replaced Pi by tau you need a way to convert it to a numeric value when you are looking for a number. Without this, Sin[1.1*\[Tau]] // N won't return a numeric value. There are other things needed to get it to act just like Pi behaves. $\endgroup$
    – Bob Hanlon
    Commented Mar 28, 2023 at 19:58
  • $\begingroup$ @BobHanlon I defined t:=2 Pi and when I write Sin[1.1t]//N, it gives ≈0.5877, which is the correct numeric value. Am I missing something? $\endgroup$
    – Vestoo
    Commented Mar 29, 2023 at 15:32
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    $\begingroup$ $Post = (# /. {\[Pi] -> \[Tau]/2, str_String?(StringContainsQ[#, "\[Pi]"] &) :> ToString[ToExpression[str] /. \[Pi] -> \[Tau]/2, TraditionalForm]}) &; $\endgroup$
    – Bob Hanlon
    Commented Mar 29, 2023 at 16:28

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