If we define circumference as C = τr, then we can actually just use the general formula for an area of a polygon (A = 1/2 p a), which for a circle (infinite-sided polygon) becomes A = 1/2 τr r. C=p and r=a is just circle vs polygon language.
Of course πr^2 is the same formula, it’s just obscured a little bit more. But now you can see why it’s not always 2π - it’s because we actually did divide tau in half.
Anyway, I just think its kinda neat. I don’t think tau will catch on though 🙂.
Sorry, I would have done a better job, but that post was already super tedious to do in mobile. And r is the only variable I failed to define at all, but I figured people with opinions on pi would already know that one 🙂
The thing is, 2π is quite often for sure, but 1π isn’t that rare and doubling is so much easier than halving that π still wins against τ
i’m in favor of renaming 2π to σ because the symbol looks like somebody is taking a measurement of the circumference of a circle.
It’s just more intuitive to use tau.
Take for example, the area of a circle.
If we define circumference as
C = τr, then we can actually just use the general formula for an area of a polygon (A = 1/2 p a), which for a circle (infinite-sided polygon) becomesA = 1/2 τr r.C=pandr=ais just circle vs polygon language.Of course πr^2 is the same formula, it’s just obscured a little bit more. But now you can see why it’s not always 2π - it’s because we actually did divide tau in half.
Anyway, I just think its kinda neat. I don’t think tau will catch on though 🙂.
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Sorry, I would have done a better job, but that post was already super tedious to do in mobile. And r is the only variable I failed to define at all, but I figured people with opinions on pi would already know that one 🙂
When it comes to pi, doubling is exactly as hard as halving.