If mathematics has a bikeshed, this is it.
I enjoy the ridiculousness of it all, but people who consider this anything other than a well-executed joke really should get a hold of themselves.
I feel very fortunate that the tau vs. pi argument was around when I went back to study math in earnest. I found tau much more intuitive and it helped me to visualize and learn the material more effectively.
I now use tau whenever I can. However, I don't find switching back and forth to accommodate pi loyalists that taxing. You don't really have to choose one exclusively.
It's just the same useless argument every year. Just use what you want. I've been taught pi since secondary school. I understand it well and can use it effectively. Never have I sat there and thought, "if only there was a shortcut to multiplying this by 2". There's whole sites, videos and movements to get tau popular. I just personally don't understand the point.
The choice between Pi vs. Tau is completely arbitrary and should be based on minimizing the friction of use. Everyone knows Pi, few knows about Tau. I see no point in spending any more energy than that on this kind of nonsense decisions.
While choice between tau and pi is arbitrary from mathematical point, things like pedagogy, notational simplicity and aesthetics matter.
The reason why I think π is probably better choice is because small multiples of constant are cognitively easier to process than fractions. 2π is easier to write and see as single object than τ/2. All we need to do is to make slight cognitive adjustment and think and teach 2π as a number instead of 2×π.
I just wish instead of celebrating these days on arbitrary month/day combinations, that we'd instead use some physics or math based use of them. Pi day should be when we've gone half way around the Sun and Tau, New Years Day.
As today tauday is tuesday,
the Angle programming language now knows tau:
⦠ assert tau / 2 = pi
True
I'm in favor of keeping pi because of one simple equation:
e^{i\pi} + 1 = 0
e^{i\pi} + 1 = 0
e^{i\pi} = -1
i\pi = \ln{-1}
\ln{x} + i\pi = \ln{x} + \ln{-1}
\ln{x} + i\pi = \ln{-x}
I'd rather multiply by 2 75% of the time than divide by 2 25% of the time (just a wild-ass guess of how often one or the other appear in common equations)
On to more important matters, Gamma function or Pi function?
http://mathoverflow.net/questions/20960/why-is-the-gamma-fun...
Obviously, the Pi function is the right one since Pi(n) = n! for all integers n.
Using tau would uglify euler's equation, wouldn't it?
Angular frequency (ω = 2πf) is related to this:
https://en.wikipedia.org/wiki/Angular_frequency
Note how convenient ω is when squared, in the expression of angular acceleration, eliminating a ridiculous 4 factor.
OT, but Michael Hartl's RoR tutorials are amazing and helped me learn so quickly. Worth checking out[0] if you're looking to learn
i totally suck at math, however i think i know what is a circle, i can draw one with a compas. then i think i know what is the diameter of this circle, i can draw it by drawing two more circles and a line with a ruler. because a mathematician told me that the product of this diameter by a number is the circumference of the first circle i believe him, but if another mathematician ask me to draw two more circles and another line to define the same circumference... i will probably believe that the first one suck less than the second one at maths! (sorry for my english!).
Pi is better because 'a slice of pie' links nicely to radius and makes it easy for kids to remember. QED.
Wow, they've really redesigned that site's look. Not sure I like it... the figures especially look bad.
What's a nice infinite series summing to tau that isn't merely 2S(n) where S(n) sums to pi?
Okay, tau is a little better.
Meanwhile, millions of lines of code are written in languages with no type system to speak of, millions of Americans use imperial measurements, billions worldwide speak languages that are inefficient and ambiguous, and many many people aren't even educated enough to know about pi or tau.
We have much more damaging problems than multiplying by 2. Given the gigantic amount of effort it would take to fix this one, I think that effort could be better spent.
I have found the idea of tau useful even though I have never used it in writing.
One argument in favor of tau is that in many formulas pi often has the multiplier 2 in front of it. If these formulas are written in terms of tau, they may become slightly easier to memorize and manipulate. Perhaps so, but I don't really care about this. It’s not a big difference. Besides, there are also lots of formulas that are easier to memorize and manipulate using pi instead of tau. The probability density function of the standard Cauchy distribution f(x) = 1/pi * 1/(1 + x^2) is one example.
However, to get a deep understanding of mathematics, I want to understand the connections between different parts of mathematics. If I see a mathematical formula with the constant pi in it, I ask myself: "How is this connected to circles?" The idea of tau taught me that that 2pi is the natural state of affairs. If I see pi by itself, I need to ask myself: "How is this connected to half-circles? Or has the multiplier 2 been cancelled away?”
So, why does the pdf of the standard Cauchy distribution above contain pi instead of 2pi? What is the standard Cauchy distribution anyway? Take a gun that shoots particles in random directions, and place it one unit distance away from an infinitely long wall. Standard Cauchy distribution is where the particles will hit the wall. The particle will only hit the wall if it is shot in a direction towards it. This corresponds to 180 degrees - and there you have it: the connection to half-circles. Of course, you also have to work out the technical details. But on an intuitive level, when I see pi in the pdf of the standard Cauchy distribution I don’t think about how the missing multiplier makes it easier to remember a bunch of symbols; I think of particles hitting a wall.