Admittedly, it doesn't do it very well, except for the point made that all of mathematical calculations involving circles use the radius as the standard, while pi uses the diameter.
The problem, as she said, is that we have been doing it for years.
It makes far more sense to use tau, because it is the ratio of the radius to the circumference rather than the diameter. Blame the ancient Greeks for this. Today, we don't do ANY calculations using the diameter.
I'm gonna go with the two-thousand year mathematician consensus that pi is best, rather than a few cranky modern semi-math literate folks who insist tau is best.
One of my favorite tales a preacher I knew loved to use as an example. To actually fight the whole thing of blindly following previous generation examples.
He was visiting a family..and saw the wife cooking, she took a whole gorgeous hamhock...chopped off a good 1/3 of it, threw that away, and then proceeded to cook the rest. So the preacher asked 'why didn't you cook the entire thing?'. Reply?
Well, my mother cooked it this way her whole life, so that must be the right way to do it.
Now..the preacher wasn't satisfied..so convinced her to get the reason from her mother. Her reply "well my mother always cooked it this way, so that's just the way its done.".
So finally he convinced them to ask the grandmother in this case. Her response?
"Oh sweety, I always cooked it like that because the pot I used wasn't big enough to cook the whole thing."
So we had a couple of generations of people..wasting a good 1/3 portion of meat...because the first generation never had the proper utensils to cook the whole thing.
Sometimes it is good to look back at tradition and actually ask 'what is the basis of this tradition' in this case...if Tau makes the formula make more sense..look better, be easier to remember..and actually fall better in line with the rest of the math equations of its type...why continue to use Pi?
So the answer shouldn't be 'because Pi was used before' it should be 'because Pi does _this_ thing that makes it the better choice'.
as for how you find the area of a circle with a Tau? Until I re-learn how to construct a proof of what happens when you integrate a circular function, I'd just have to assume you'd get 1/2*Tau*r^2.
Which starts to look like a formula for kinetic energy or the displacement of a free-falling object.
Don't look at me, I haven't read it, I don't have the proofs to back it up, and I can't explain the whys and wherefores, I just know it looks like some of the stuff I learned a good while ago.
Most equations involving Pi...are built with the idea of actually using 2Pi..not just Pi. And that if you just used 2Pi (called Tao) as a constant, many many equations that involve Pi would look much cleaner..and would fit in with the rest of math and its equations better.
rhjunior
The problem, as she said, is that we have been doing it for years.
It makes far more sense to use tau, because it is the ratio of the radius to the circumference rather than the diameter. Blame the ancient Greeks for this. Today, we don't do ANY calculations using the diameter.
What about surface area? Pi*r*r
How would Tau fit into this?
Remember, at one time things like Pi and the pythagorean theorem were both mathematical heresies...
He was visiting a family..and saw the wife cooking, she took a whole gorgeous hamhock...chopped off a good 1/3 of it, threw that away, and then proceeded to cook the rest. So the preacher asked 'why didn't you cook the entire thing?'. Reply?
Well, my mother cooked it this way her whole life, so that must be the right way to do it.
Now..the preacher wasn't satisfied..so convinced her to get the reason from her mother. Her reply "well my mother always cooked it this way, so that's just the way its done.".
So finally he convinced them to ask the grandmother in this case. Her response?
"Oh sweety, I always cooked it like that because the pot I used wasn't big enough to cook the whole thing."
So we had a couple of generations of people..wasting a good 1/3 portion of meat...because the first generation never had the proper utensils to cook the whole thing.
Sometimes it is good to look back at tradition and actually ask 'what is the basis of this tradition' in this case...if Tau makes the formula make more sense..look better, be easier to remember..and actually fall better in line with the rest of the math equations of its type...why continue to use Pi?
So the answer shouldn't be 'because Pi was used before' it should be 'because Pi does _this_ thing that makes it the better choice'.
... cake are squared.
as for how you find the area of a circle with a Tau? Until I re-learn how to construct a proof of what happens when you integrate a circular function, I'd just have to assume you'd get 1/2*Tau*r^2.
Which starts to look like a formula for kinetic energy or the displacement of a free-falling object.
kE=1/2*M*v^2
S=1/2*A*t^2
Most equations involving Pi...are built with the idea of actually using 2Pi..not just Pi. And that if you just used 2Pi (called Tao) as a constant, many many equations that involve Pi would look much cleaner..and would fit in with the rest of math and its equations better.