Pi to 6600 digits
Fortunately, the cosmos is forgiving enough that we don't need to know pi to the last digit to produce practical results.
Due to the importance of pi to our understanding of the universe, March 14 — 3-14 — was chosen as "Pi Day", to celebrate this mathematical constant. And how do you celebrate such a thing? Typically, with pie!
Pi Pie Koka Sexton
Pi pie, courtesy koka_sexton/Flickr
The significance of a Pi Day Eclipse?
Pi is used in computing a lot of things in science. Anything that involves circles, ellipses, or curves will have Pi somewhere in the equation.
This applies to weather, with the coriolis effects of the atmosphere's motion on our rotating planet.
It also factors heavily in the calculations of the orbits in the solar system. In this case, we couldn't properly calculate the orbit of the Moon around Earth, and the Earth around the Sun, without knowing the value of pi.
Moon Orbit - Earth Shadow - Total Lunar Eclipse
The shape of the Moon's orbit around Earth, the angle of the sunlight, and the size and shape of Earth's shadow are all computed using pi. (NASA's Scientific Visualization Studio)
The fact that we do know pi means that we can use the equations of planetary motion to predict lunar eclipses and solar eclipses, years, decades, or even centuries out. We know the size and shape of Earth's shadow due to pi, as well, which is crucial in figuring out the exact timing of a total lunar eclipse.