Comment by karmakaze
1 year ago
Might be interesting if were true in Planck units.
But also 2Pi is fundamental, who defines a ratio of something to 2 of something (radius)?
1 year ago
Might be interesting if were true in Planck units.
But also 2Pi is fundamental, who defines a ratio of something to 2 of something (radius)?
No, Tau is fundamental. Pi only exists because someone mistakenly thought the formula for circumference involved diameter, when in fact it involves radius. ("Quit factoring a 2 out of Tau!" I tell them.)
Eh, you can find plenty of cases where tau is just as awkward as pi is elsewhere. Right off the bat, the area of a circle becomes more awkward with tau, becoming (tau*r^2)/2, and in general, the volume of an n-ball gains weird powers and roots of two in its denominator as n increases if you switch to tau. In general, I don't think you can really claim either one is "more fundamental". It's just a matter of framing.
Actually, no: that Tau-centric area formula you gave derives naturally from taking the integral. Your example actually fits the expectation you have from what you learned in Calculus I. You should _expect_ that 1/2 scaling to be there.
If it seems awkward to you, it's only because of a lifetime of seeing it done in terms of pi.
1 reply →
In case you didn't see this:
https://tauday.com/tau-manifesto
And this is the section that addresses your point:
https://tauday.com/tau-manifesto#sec-circular_area
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It's not really about being awkward (that's a tell not the motivation), it's about basing on a radius or diameter: which is more fundamental? Or the arc length of a unit circle or half a circle, which isn't an arbitray formula it's the definition.
Any examples of textbooks or papers where the author used tau instead of pi (and the topic was not tau or pi)?
There might be, I don't know. But as you're already aware, we are culturally stuck with pi and so that's how it is taught.
That was (obliviously?) my point.