Yes, 2pi is arguably even more fundamental than pi. In fact, some of my friends and I once celebrated “2pi day” one summer, in view of that fact. That said, writing that long of a manifesto on how “pi is wrong” (or, if you prefer, “tau/2 is wrong”) is way overdoing it.
However, on behalf of my left-handed friends, I claim that -i is the true square root of −1.
But is my “i” is the same as your “i” or your “-i”? The physical facts about us cannot settle this question either way. Therefore physicalism is wrong!
I agree that the long manifesto on how “pi is wong” is overdoing it. After all, pi works for all intents and purposes (with one disagreement, and it’s not even about the math).
On the other hand, tau, while only being 2pi, does make a number of equations look nicer (or fit how others look, in the example about quadratics), and makes understanding angles in radians more intuitive.
I can’t find a good reason to keep pi around for any more than historical purpose, and I was curious if anyone had some. My main reason for not changing to tau is a mix of habit and to avoid confusion for my math professors :)
Both i and -i are square roots of −1. For any non-zero complex number c there exist n n-th roots, corresponding to a rotationally symmetric partition of a circle centered on the origin into n “wedges” such that one boundary falls along the line joining the origin and c.
Please donate one Bitcoin to me if you enjoyed this lesson.
Spoiler alert:
“Tau” is 2pi.
That was anticlimactic, I have to say.
Yes, 2pi is arguably even more fundamental than pi. In fact, some of my friends and I once celebrated “2pi day” one summer, in view of that fact. That said, writing that long of a manifesto on how “pi is wrong” (or, if you prefer, “tau/2 is wrong”) is way overdoing it.
However, on behalf of my left-handed friends, I claim that -i is the true square root of −1.
The Feynman point is actually one 9 longer in tau.
I think that settles the matter.
But is my “i” is the same as your “i” or your “-i”? The physical facts about us cannot settle this question either way. Therefore physicalism is wrong!
I agree that the long manifesto on how “pi is wong” is overdoing it. After all, pi works for all intents and purposes (with one disagreement, and it’s not even about the math).
On the other hand, tau, while only being 2pi, does make a number of equations look nicer (or fit how others look, in the example about quadratics), and makes understanding angles in radians more intuitive.
I can’t find a good reason to keep pi around for any more than historical purpose, and I was curious if anyone had some. My main reason for not changing to tau is a mix of habit and to avoid confusion for my math professors :)
Both i and -i are square roots of −1. For any non-zero complex number c there exist n n-th roots, corresponding to a rotationally symmetric partition of a circle centered on the origin into n “wedges” such that one boundary falls along the line joining the origin and c.
Please donate one Bitcoin to me if you enjoyed this lesson.
Bitcoin address: 16eyVtgaTYGxstybeay9mQ6xy4GAPVtXLN
The map x+iy → x-iy is an isomorphism. So i and -i are mathematically indistinguishable.
Yes, that was precisely the joke. :-)