TITLE: Why is $\pi$ = 3.14... instead of 6.28...?
QUESTION [26 upvotes]: Inspired by a paper (from 2001) entitled Pi is Wrong:
Why is $\pi$ = 3.14... instead of 6.28... ?
Setting $\pi$ = 6.28 would seem to simplify many equations and constants in math and physics.
Is there an intuitive reason we relate the circumference of a circle to its diameter instead of its radius, or was it an arbitrary choice that's left us with multiplicative baggage?

REPLY [11 votes]: For those stating that $\frac{\tau}{2}r^2$ is more cumbersome than $\pi r^2$ I would like to point out that the factor of $\frac{1}{2}$ is found naturally in many equations throughout physics and goes to show a fundamental relationship between the the area of a circle and the rest of physics that we miss when we cover it up with $\pi$. For example:
$\frac{1}{2}mv^2$ = kinetic energy, where $m$ is mass and $v$ is velocity.
$\frac{1}{2}kx^2$ = potential energy stored in a spring, where $k$ is the sprint constant and $x$ is displacement.
$\frac{1}{2}at^2$ = displacement, where $a$ is acceleration and $t$ is time.
That missing factor of $\frac{1}{2}$ shows an important relationship between the area of a circle and the rest of physics, something we've been missing due to our adherence to an old way of looking at circles. We don't make circles using their diameter, regardless of how easy diameter is to measure, we make circles using the radius. When you consider that all important factor of $\frac{1}{2}$ and you use $\tau \approx (6.28)$ instead of $\pi \approx (3.14)$ the area of a circle becomes $\frac{1}{2}\tau r^2$