Greetings!
This is Sci Show and if you’re watching this you’re probably interested in
things like science. This means you
should know about Pi. It’s very important stuff! It is the Circle Constant
after all... Or is it? What if Pi is only half the story...
[Intro]
We've all heard of Pi. It’s 3.1415 and so on, it’s fundamental to geometry, and it even
has a day named after it. Another thing you may have noticed is that quite a
lot of equations using Pi actually use 2Pi. This is because Pi is defined as
the circumference of a circle over its diameter, while in math what you often
need is circumference over radius, which is twice as large. As a result there
have been attempts to introduce a new constant – Tau – which has a value of 2Pi.
Now
I know what you’re thinking! – Why do we need a new constant when we can just
multiply by two? After all: we've already mastered the arcane art of doubling;
why not use it? Well there are reasons...
Number
one: Tau is easier to teach. This may not seem all that apparent to you; after
all, this would mean re-learning all your formulas. But that’s not the point!
The idea is that, when first introduced to geometry kids might have an easier
time using Tau. For example: If you’re
measuring angles in radians you’ll find that Pi radians only take you halfway
around the circle and that’s no fun. If you want a full circle you use 2Pi
radians and for a quarter of a circle you need half of Pi. You can see why this
might confuse someone who’s learning this for the first time. Tau, however,
does not require that a student always remember that factor of two. A circle is Tau
radians, half a circle is half of Tau, and a quarter-circle is a quarter of
Tau.
Number
two: Pi obscures useful information. If you remember your first few geometry
classes you might have realised that the area of a circle is an
excellent example of Pi’s ability to stand on its own. The area of a circle,
dear viewers, is πr^2. Despite this, the supporters of Tau
seem unfazed. In fact, in the Tau Manifesto (link in my pants area), one
physicist claims that the area of a circle is a quadratic form and should be given the
same treatment physics reserves for other quadratic forms. As you’ll notice in statements
such as: “distance fallen in uniform gravity = 1/2gt^2”, “kinetic
energy = 1/2mv^2”, and “potential energy
in a spring = 1/2kx^2” – the first
value is halved while the second value is squared. He proposes that we treat
the area of a circle this way and write it out as A=1/2τr^2.
Following
so far? It get’s weirder.
Number
3: It augments Euler’s identity. There’s a little equation in math
called Euler’s identity which
is often referred to as: “the most beautiful equation in mathematics”.
In its most basic form, Euler’s
identity states that: e^iπ = -1. This is then
rephrased as e^iπ +1 = 0. As before
with the area of a circle, the Tau Manifesto argues that information is
missing. If Euler’s identity is rewritten as e^iτ = 1 it
shows something truly remarkable: as the angle increases from half-Tau to Tau,
the resultant value progresses from negative one into positive one. In
math-words this means that “the complex exponential of Tau is unity”. In English this means that when you use
Tau you get exactly one unit and when you use Pi you get the reverse.
That concludes this episode of Sci Show! If you
want to keep getting smarter with us you can go to youtube.com/scishow and
subscribe. If you have suggestions for future videos, leave them in the
comments. If you want to debate the merits of Tau and Pi you can use the
comments for that too or you can take the discussion to Facebook, Twitter, and
Tumblr. Links to the Tau Manifesto and, it’s mortal enemy, the Pi manifesto in
the description. There are also videos on this topic. Click to the right of me
to see one by numberphile and click to the left to see one by Vihart. And, as
always, thanks for watching!
Pants links:
If you believe this write-up is too complicated for your audience I can write on other topics. I just used this as the example because it was the only topic I could think of at the time (blame Vihart). I sometimes over complicate things when I talk math (which is odd since I'm a math tutor).
The style of prose used is indicative of what I can write. I can change a few things (eg. drop the credits) but this is generally the way my writing sounds. If you like it, I can start writing any time. My preferred subjects are Math, Chemistry, Biology, Astronomy, and Technology (I'm not sure whether Economics qualifies) so you can expect to see a lot of those. I can also write on many other subjects if given enough time to research my material.
Thank you for taking the time to read this and don't forget to be awesome =D
