Pi day is here once again on March 14, 3/14 and I have scoured various interesting articles for engineers regarding this mathematical number.
When I first heard of Pi in grammar school, it was presented to us in class as 22/7, a seemingly ordinary ratio of two numbers. Little did I know back then how important it would be to my career as an engineer.
The Greek symbol Pi, π , has been the source of many articles over the years. Steven Bogart, a mathematics instructor at Georgia Perimeter College, wrote an article in Scientific American entitled What is Pi, and how did it originate?. In his article Professor Bogart states the following:
According to Petr Beckmann's A History of Pi, the Greek letter π was first used for this purpose by William Jones in 1706, probably as an abbreviation of periphery, and became standard mathematical notation roughly 30 years later.
NASA has also chimed in this year with a really nice article about how to Celebrate Pi Day like a NASA Rocket Scientist
Here is an example of finding out how many times the Mars Rover’s wheels have rotated in its lifetime on the Red Planet:
So how many decimal places must we use for Pi? NASA JPL’s director and chief engineer for NASA's Dawn mission, Marc Rayman, puts this in perspective; Let me summarize his article, How many decimals of Pi do we really need?:
- For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793.
- The spacecraft, Voyager 1 is the furthest space vehicle from Earth right now at approximately 12.5 billion miles away +/- around a million miles. Take a circle with a radius of exactly that size (or 25 billion miles in diameter) and let’s calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, we get a bit more than 78 billion miles. We don't need to be concerned here with exactly what the value is but rather what the error in the value is by not using more digits of pi. So we try cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches, somewhat less than the length of your little finger.
Read the entire article---it’s inspiring.
Want to see the square root of 2 to 1 million digits? Click on this link
I hope you enjoyed this article. Please share your Pi stories with our readers in the comments below. In order to comment, you will have register on Planet Analog if not already registered.
And remember, “Pi are not square, Pi are round!”