4 ms·

It seems like these guys are fighting an uphill battle, not that I'd want to discourage it. It's simply much easier to visualize the path traced when you relate

It seems like these guys are fighting an uphill battle, not that I'd want to discourage it. It's simply much easier to visualize the path traced when you relate the radius to the circumference of a circle rather than its diameter, since there's only one point to focus on at a time as you rotate around the axis. Pi is insidious as it's only much later that this foundation begins to appear problematic. [My analogy was not very good. The circumference is the only dimension of a circle stated in terms of diameter, not radius, and so substituting tau for pi is simply relating the radius of a circle to its circumference instead of its diameter. Circumference = tau * radius. This has the benefit of bringing the circumference formula in line with all the other circle equations. When we look at the area of a circle, tau is not very intuitive, however. The formula for the area of a circle uses the square of the radius, so there's not an intuitive way to factor two into the equation without just making extra mental work for yourself. For volume, the effect is somewhat neutral. Volume = 4/3 pi * radius^3 = 2/3 tau * r^3. 2/3 vs. 4/3 doesn't seem to add much insight into the equation. Circumference = tau * r Area = 1/2 tau * r^2 Volume = 2/3 tau * r^3 4th dimension circle = 3/4 tau * r^4? : P Maybe there's something to this...]

blahedo 14y ago
No, the tau manifesto agrees: radius is the more fundamental concept. That's why tau is better! Pi is an expression relating the diameter to the circumference, which as you point out is a little counterintuitive.
- Retric 14y ago
  The problem with tau for introductory math is area = pi * r^2 = (tau/2) * r^2. Given the choice between having equations with 2x or other with 1/2 y most people feel more comfortable with 2x. EX: e^(i * tau / 2) = -1 wait what?
  - bascule 14y ago
    If you read the Tau Manifesto you'll see why tau * r^2 / 2 is actually AWESOME (he actually refers to it as pi's coup de grace) Just think of it like an integral (that's what it is, after all!), raise the power and divide by the power. Suddenly the origin of this formula is no longer obscured. Regarding Euler's identity: e^(i * tau) = 1
    - deleted 14y ago
      [deleted]
    - Retric 14y ago
      Telling a 3rd grader to think of it like an integral seems to be putting the cart WAAAAAAAY before the horse. Edit: Also that's is hardly a more fundamental equation because you could also say e^(1024 pi * i) = e^(4096 * tau * i) = 1.
      - bascule 14y ago
        It won't amaze third graders, but it would make a lot more sense the first time you learn integral calculus
        Retric 14y ago
        Meh, so did 2 * pi * r > 2 * pi * (r ^ 2) / 2 = pi * r ^ 2. The great thing about math is it's it works out either way. So, it really comes down to which is easier to deal with and students seem to have an easier time remembering and understanding 2pir and pi*r^2, but in the end it's tau day so that's what people want to argue about.
        bascule 14y ago
        "students seem to have an easier time remembering and understanding 2 pi r and pi r^2" Are you speaking from empirical experience as a math teacher? What makes 2 pi r easier to understand than tau r?
        fryguy 14y ago
        Also perhaps, make integral calculus make more sense?
      - waterhouse 14y ago
        Eh, 3rd graders can probably handle the area of a triangle, which can be viewed as a definite integral. (Somehow, middle school physics students seem to be able to handle computing the distance traveled by an object given starting velocity and constant acceleration--again, technically an integral.) In fact, one can view a circle as being made up of a bunch of really thin triangles (this is how one usually derives the area of a circle), and this again is something that third-graders can appreciate--cut a paper circle into slices, and see if you can get the slices to look more and more like triangles as you cut them smaller. (I vaguely remember doing something like this in elementary school.)
  - aidenn0 14y ago
    We should thus not teach anyone the formula for area of a triangle then
    - Retric 14y ago
      The area of a triangle does not have both a constant and a division by 2.
WiseWeasel 14y ago
I wonder if the fourth dimension in this case might be the maximum internal surface area or something of the sort. A fourth dimension perfect circle looks like a sphere at first glance, but has the maximum possible internal surface area upon closer inspection.

blahedo 14y ago

No, the tau manifesto agrees: radius is the more fundamental concept. That's why tau is better! Pi is an expression relating the diameter to the circumference, which as you point out is a little counterintuitive.

Retric 14y ago
The problem with tau for introductory math is area = pi * r^2 = (tau/2) * r^2. Given the choice between having equations with 2x or other with 1/2 y most people feel more comfortable with 2x. EX: e^(i * tau / 2) = -1 wait what?
- bascule 14y ago
  If you read the Tau Manifesto you'll see why tau * r^2 / 2 is actually AWESOME (he actually refers to it as pi's coup de grace) Just think of it like an integral (that's what it is, after all!), raise the power and divide by the power. Suddenly the origin of this formula is no longer obscured. Regarding Euler's identity: e^(i * tau) = 1
  - deleted 14y ago
    [deleted]
  - Retric 14y ago
    Telling a 3rd grader to think of it like an integral seems to be putting the cart WAAAAAAAY before the horse. Edit: Also that's is hardly a more fundamental equation because you could also say e^(1024 pi * i) = e^(4096 * tau * i) = 1.
    - bascule 14y ago
      It won't amaze third graders, but it would make a lot more sense the first time you learn integral calculus
      - Retric 14y ago
        Meh, so did 2 * pi * r > 2 * pi * (r ^ 2) / 2 = pi * r ^ 2. The great thing about math is it's it works out either way. So, it really comes down to which is easier to deal with and students seem to have an easier time remembering and understanding 2pir and pi*r^2, but in the end it's tau day so that's what people want to argue about.
        bascule 14y ago
        "students seem to have an easier time remembering and understanding 2 pi r and pi r^2" Are you speaking from empirical experience as a math teacher? What makes 2 pi r easier to understand than tau r?
      - fryguy 14y ago
        Also perhaps, make integral calculus make more sense?
    - waterhouse 14y ago
      Eh, 3rd graders can probably handle the area of a triangle, which can be viewed as a definite integral. (Somehow, middle school physics students seem to be able to handle computing the distance traveled by an object given starting velocity and constant acceleration--again, technically an integral.) In fact, one can view a circle as being made up of a bunch of really thin triangles (this is how one usually derives the area of a circle), and this again is something that third-graders can appreciate--cut a paper circle into slices, and see if you can get the slices to look more and more like triangles as you cut them smaller. (I vaguely remember doing something like this in elementary school.)
- aidenn0 14y ago
  We should thus not teach anyone the formula for area of a triangle then
  - Retric 14y ago
    The area of a triangle does not have both a constant and a division by 2.

WiseWeasel 14y ago

I wonder if the fourth dimension in this case might be the maximum internal surface area or something of the sort. A fourth dimension perfect circle looks like a sphere at first glance, but has the maximum possible internal surface area upon closer inspection.