So it is PI Day and I thought I would write something up about PI.
First, what is PI? PI is a number that is the exact ratio between the diameter and the circumference of a circle or the distance across to the distance around. PI is an irrational number meaning that its precise number in decimal notation is infinitely long and will never repeat. So PI is the best way to get a glimpse into the mind of God and how He designed this grand part of the world.
Second, PI... is it 3.14 or is it 3.14159 and what does that matter? This comes into accuracy and precision. Accuracy is the closeness of a measured value to a standard, think of hitting a bullseye. Precision is the closeness of measurements to each other, think of grouping all of the hits on a bullseye near each other but not on the bullseye. When a measurement is both precise and accurate then it will would be the center of a bullseye. The greater number of decimals used with PI would increase the accuracy of the number.
So it would appear that using a more accurate number of PI would be beneficial, but when you start using highly accurate numbers with computers issues with data types begin to come into play. Depending on the data type, the processor on the computer will have optimization for doing the calculations. Float for example is used for high performance but isn't accurate. This would mean that even if a highly accurate number with PI is used with a float will not generate precise or accurate numbers.
So how accurate is too accurate? Well, suffice to say there is a certain point of diminishing returns for using a highly accurate number of PI. So according the the Jet Propulsion Lab, fifteen decimal places will calculate the a circle that is 78 billion miles around with the accuracy of 1.5 inches. If PI with fifteen decimal places is used to calculate a circle that can fit on the earth, it will have an accuracy to within one molecule. Forty-six decimal places of PI is able to calculate a circle to an accuracy of less than the diameter of a hydrogen atom for a circle that would just fit within the entire visible universe.
So the reality of the world is, 3.14 is a great number and a precise number for every day life.