Half Tau Day Pi Lie?
Half Tau Day Pi WHY the Lie?
The next time your teacher says, "because it is..."
Think twice. Think thrice...
So my sister phones me up and asks me, "Do you know what day it is today?".
Of course I do, Its the 28th of June. Exactly one month away from my birthday, 4 weeks away from the school holidays, and...
No, no, she says, "What Math day is it today?"
For the life of me, I had no idea! The first thing I did was ask everyone on our facebook wall. We had some good guess's.
"Its Tau day", she says!
Well, what the heck is that?
Its 2×pi apparently.
So what! I think to myself!
Its just they are considering replacing Pi for Tao. Whoooww...Hang on a minute. They can't do that? Can they? Pi is huge. Its used in everything.
But, Yes, my sister is right. There is a huge campaign out there to put the record straight.
Researchers have apparently discovered that Tao, τ, is more important and widely used than Pi. On top of that, we have been using Pi incorrectly. Yes incorrectly. All those years of Pi sums, to now discover that we have all been doing it wrong. So, my teacher was wrong after all. So was everyone else!
Pi is wrong!
Yet, everyone loves it. It has an infinite number of places. Even though we approximate it with 3.14. It features in movies and books and even has its own day.
Pi day is on March 14th. They chose that day because of the number of Pi estimated at 3.14 (if you've not figured it, march=3rd month, 14th=.14 hence 3.14). And is it just a coincidence that Tao day is on the 28th, nope. Tao=6.28... which is obviously double Pi.
Pi is used through out maths.
The Normal Distribution
Cauchy's Integral Formula
The Gauss's Law
Reduced Planck Constant
But wait, stop! Its not just Pi that appears. Its 2 times Pi, check it out.
We all know that Pi is defined as the ratio of a circle's circumference to it diameter:
In other words, if we take any circle.
Any size, any shape.
If we measure round the edge (circumference).
Then divide it by the diameter...it is always 3.14, how clever is that hey.
However, this is where the problem lies, because the true circle number is the ratio of the circles circumference to its radius and not its diameter.
A Waste of Paper
The thing is, Pi is too important to just erase it from the world. Besides, too many books would be wasted, can you imagine the devastation of the rain forest of having to burn so many books due to one letter.
It's weight is so heavy. Its centuries years old. Why has nobody discovered this mishap till now? Why?...Because there is some huge conspiracy to promote the Pi.
Can you believe it, even google changed their logo on Pi Day of 2010 in honor of π. Check out the logo. Nice.
People even learn Pi to hundreds of places. The worst thing is, how sad is it when people start to memorize things that are not even right:
Its the wrong number when choosing to associate it with a circle. The most natural number to associate with a circle is Tao, τ=circumference/radius. Rather than Pi which is π=circumference/diameter.
A circle is defined as the collection of points that are a common distance of the radius from the center.
You can't define a circle using the diameter, since there exist shapes which have a constant diameter that arent circles.
For example a 50p coin has a contant diameter all round the shape, but it is not a circle.
As soon as we can define a circle we can define τ.
To define Pi, first we would need to define the diameter as twice the radius.
In other words we can define τ before π. So therefore τ is more natural.
So what! Whats the big deal? It just means we don't have to write an extra 2 in all the formula. Yipee.
Mathematician's Use Radians
Psst, Here comes the Hard bit!
But wait, τ begins to show its magic when we use angles. Mathematicians don't use degrees when measuring angles, but radians.
There are 360 degrees in a circle, just as there are 2π radians in a circle.
So in a quarter of a circle there are 1 quarter times 2π radians, that is π/2 radians.
In other words if we use π as the constant associated to a circle then a 1/4 of a circle corresponds to half the circle constant.
1/4 circle gives 1/2π radians. A 1/4 corresponding to a 1/2 is pure ridicules.
How about 3/4 of a circle? That corresponds to 1/4 times 3/4 π radians, which is 3/2π radians. Which is ridicules again!
What do you think 1/3 π radians gives? its 1/6 of a circle. Definitely potty.
And so on.
Tau is the Natural Choice
Now lets see what happens when we use τ. Whats is 1/4 of a circle when using τ? Well, its 1/4 τ radians.
How about 3/4 of a circle? Its 3/4 τ radians. Easy.
What about 1/6 τ radians? Well its 1/6 of a circle.
And a really hard one, what is 4/21 of a circle in terms of τ radians? Yes, thats correct, 4/21τ. See how easy was that!
I remember when I was first learning radians and π. It was so confusing and illogical because of that factor 2. Is it anyway wonder math has such a bad name when we have to learn stuff that doesn't even make sense.
With Tau it becomes simpler: Half a turn of a circle is simply 1/2 τ radians.
Easy as PIe! No pun intended ;)
You maybe right!
So, the morale of the story. Next time you question whats what and whats not and your teacher says, 'because it is'.
Maybe it isn't.
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