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This should probably link to the actual section of the page that was added: http://tauday.com/tau-manifesto?new#sec:getting_to_the_botto...
I live with 60 minutes per hour, 24 hours per day, 7 days per week, 360° in a full circle, a speed of light of 299,792,458 m/s, to name only a few cases of historical 'accidents'. 2π is arguably more fundamental than π, but given the things above, I don't care much. If you want to tackle something worthwhile, update theoretical physics lectures to 'modern' notation (where modern means 1960s).
360° in a full circle That's one of the things tau can help solve. I suspect the main reason that people still use degrees so much is because using pi undermines the beauty and intuitiveness of radians.
I live with 60 minutes per hour, 24 hours per day, 7 days per week, 360° in a full circle, a speed of light of 299,792,458 m/s, to name only a few cases of historical 'accidents'. 2π is arguably more fundamental than π, but given the things above, I don't care much. If you want to tackle something worthwhile, update theoretical physics lectures to 'modern' notation (where modern means 1960s).
360° in a full circle That's one of the things tau can help solve. I suspect the main reason that people still use degrees so much is because using pi undermines the beauty and intuitiveness of radians.
Earlier quoted context omitted.
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?
We should thus not teach anyone the formula for area of a triangle then
I live with 60 minutes per hour, 24 hours per day, 7 days per week, 360° in a full circle, a speed of light of 299,792,458 m/s, to name only a few cases of historical 'accidents'. 2π is arguably more fundamental than π, but given the things above, I don't care much. If you want to tackle something worthwhile, update theoretical physics lectures to 'modern' notation (where modern means 1960s).
360° in a full circle That's one of the things tau can help solve. I suspect the main reason that people still use degrees so much is because using pi undermines the beauty and intuitiveness of radians.
People can't be bothered to change, except radians are much more mathematically easy to use, so people who need to do advanced maths will use it.
However, laziness is also the reason why people don't change to tau. tau is just a multiple of pi. Confronted with such a small change, people will just think that they can't be bothered to change, especially since pi is already widely supported and implemented in any of the tools that we use, and tau is not.
There's no way that changing to tau will make more people use radians.
Earlier quoted context omitted.
360° in a full circle That's one of the things tau can help solve. I suspect the main reason that people still use degrees so much is because using pi undermines the beauty and intuitiveness of radians.
No, the main reason why degrees are still in use is because most people have an easier time with 51° instead of 1/7 τ.
Earlier quoted context omitted.
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
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.
Earlier quoted context omitted.
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
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.
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.)
Earlier quoted context omitted.
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.
It won't amaze third graders, but it would make a lot more sense the first time you learn integral calculus
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.
Earlier quoted context omitted.
No, the main reason why degrees are still in use is because most people have an easier time with 51° instead of 1/7 τ.
51° is not 1/7 τ. 1/7 τ is (51 3/7)°, or 51.428571...°. If you round that to 51°, then presumably you're doing something where inexact numbers are fine, in which case you might then use "0.89 (radians)". My intuition is better for degrees here, but I think that would change if I spent ten minutes doing calculations involving real radian measures.
I could have used 0.14 τ to make my point as well: If you want to avoid fractions in common cases, you'll need to multiply with an arbitrary number like, say 100 (which has obvious benefits in a base-10 system), but arguments could be made for something like 400 (in which case we end up with gon) or, say 360, which has the benefit that it's the established standard (even though it's not the most obvious choice).
Actual radians (ie not expressed as fractions of 2π) are pretty user-unfriendly in a base-10 system.