This video has totally converted me off pi. Long live tau! 😛
carlie
Oh my (nonexistent) god. I’m pretty sure I never related a sine wave to the corresponding points on a circle, ever, and I got As in trig and calc. Dammit, it all makes sense now!
daakujc
Dont miss the last bit.. hilarious!
I mean the one at 5:10..
#winning
Adam
Oh man I wish this would be taught in schools. The Trigonometry class I’m in is so messy and it has nothing to do with its eating habits.
@carlie You never related the two? :S Weird!
daakujc
@carlie me neither!
Hollynoats
Wow. Too bad I didn’t understand ANY of that, it seems like it may have been interesting.
It’s sort of like Planck’s constant (h), which is nearly always replaced by the far more useful Planck’s reduced constant (h-bar = h/2pi). Unfortunately, there are a few contexts where this results in writing 2pi*h-bar all over the place.
You know what would be great? If it were possible to set pi=tau=1, just like we set the speed of light to 1 by appropriate choice of units.
Nakor
Using tau makes so much more sense! Why we ever related pi to a circle’s diameter rather than its radius, which is more important pretty much across the board in math, is well beyond me. (Sadly, I think I shall have to refrain from using it on Friday’s calculus final.)
Steve
Wow. This really makes tons of sense. Tau would be much more practical.
I knew of the abundance of 2*pi in all kinds of scientific formulas, but I never really thought about how much easier it could be conceptually if the definition were different in the first place
*Watches entire video*
“Uhh . . uh . . uh . . ”
*Puts fingers in ears*
“LA LA LA, I CAN’T HEAR YOU!”
CanadianNihilist
I know Hemant is a math teacher an all, but I fail to see what this has to do with religion or lack of it.
Emma
What about the area of a circle formula? A=(?/2)*(r^2) look messier than A=?*r^2. And a lot of school systems couldn’t celebrate ?-day in the school year.
But it’s a cool idea. And I really liked the bit with Euler’s identity.
@Carlie: I remember being annoyed at my highschool geometry teacher for this reason when he taught us about the trigonometry of a right triangle. He never explained exactly what cos? or sin? meant. As a result, it seemed like we entered cos or sin or tan of the angle into our calculators, and magically got a different number back that was somehow relevant to the right triangle. That annoyed me, and I wound up asking my mathematician uncle about it. Though in more advanced math classes, they did eventually explain it to us.
Steve
@Emma
As explained in the paper (see link above), using tau actually brings the area formula in line with others of the format “1/2 * x * y²”. You can find many of those in physics.
Or take Archimedes’s original proof. The area of a circle is that of a right triangle with the base as long as the circumference and a height that of the radius. Look familiar?
@Catinthewall — I showed the video to my honors’ classes today 🙂
carlie
The theoretical connection itself might have been explained to us, but the visual of moving around the circle as the wave moves down and back up again just wasn’t brought out at all (or enough for it to “click” for me). I’m a really visual learner – that would have made it so much easier to me to understand what was going on.
The only problem that matters in the tau vs. pi debate is: can both be celebrated equally easily in schools. Answer: no (in the US). tau-day would take place at the end of June: during most kids’ summer vacations.
Kidding of course, but that *is* something of a detriment. Solution? Year-round school. 😉
Charon
Nooo! Look, I agree the radius is the fundamental thing about a circle, but we can’t put another Greek letter out of use! We can’t afford it! Tau is already optical depth! (And a time constant, and torque, and probably a bunch of other stuff too.)
Greek letters are a precious commodity in science and math. I absolutely refuse to support tau day. Now, if they invent their own new symbol, then fine. Go for it.
lauren
<3!
I had been reading somewhere about this and shrugged it off. but this vid changed me! Her vids are always great.
TychaBrahe
This is the best math I have seen since Donald Duck in Mathmagicland.
my thought process was going “geeze she’s so smart, it’s incredible how well she explains this and so quickly, and makes so much sense, and… wait… did she just use that stupid Charlie Sheen catchphrase?…” *facepalm*
stogoe
I wanted to celebrate i-day, but they said I just imagined it.
Steve in SA
but Tau day is awfully close phonetically to Towel day (May 25th).
Frank Rapp
Also, 6 and 28 are the first two perfect numbers. Not to mention that my birthday is June 28. Perfect!
parv
Area of circle of radius r is given by formula …
pi * r^2
… so what point, if any, did I miss in Emma’s post about area of circle?
Steve
@parv
If you use tau, it becomes “1/2 * tau * r^2”, which is slightly more complicated, but actually more similar to many other equations
The unit circle and consistency with quadratic forms are pretty convincing arguments. I find the integrals presented misleading because common solutions often involve just a signal pi and not 2 pi. An example would be the gamma function of 1/2… which is sqrt(pi). This might turn into a classic case of cherry-picking.
Kim
We had this exact discussion the other day … that the fundamental thing that should have been defined is the circumference divided by the radius, not the diameter. I totally “get” what you mean.
However, historically, it must have been a lot easier to measure the diameter of a round thing than to measure the radius. The ancients who first noticed this ratio probably hadn’t invented trig, so the ubiquity of the radius was not there yet. They could more readily see the diameter. Of course, I’m totally speculating here.
BTW, at 0:16 in the video, you have a/b = pi, and it should have been b/a there. I see you caught the similar thing near the end and I know that you know this and were just going fast and it sort of came out that way, so no big deal.
I love your commentary as well as the idea of tau.