Eli5: I always thought pi is 22/7, but recently i found out that 22/7 is a number that is pretty close to pi, not pi itself. Then how do mathematicians found more “pi” ?
In: 167
Fun Fact!
NASA uses 15 digits of pi for calculating orbits and landing rovers on Mars.
With 40 digits of pi you can “estimate” the circumference of the known universe with error bars about the size of a single hydrogen atom.
I’m sure mathematicians have a lot of fun calculating more and more and more digits of pi, but it’s done purely for their own entertainment and bragging rights within the pi-hunter community. There is no practical use for digits of pi beyond what you could memorize in half an afternoon if you put your mind to it.
As a side note, 22/7 is ok, but a much better approximation is 355/113. It’s not too hard to remember as you start with 3 (a very approximate pi) and then do double 5’s and double 1’s followed by the last 3.
My favorite way is to run a simulation to “throw darts” randomly into a square of area 1. You throw the darts by picking a random x coordinate and a random y coordinate uniformly from the interval [0,1]. Then you can find the ratio of darts that land in the quarter circle in the first quadrant (x^2 + y^2 < 1) to the total number, and this should be the ratio of the area of the circle to the area of the square. The area of a quarter circle is pi*r^2/4 ( but r here is 1), so pi/4 and the area of the square is 1. So pi = 4*(darts in circle)/(darts in square)
I’ll just add that while calculating more and more accurate approximations of pi is a neat thought experiment, it’s not actually all that useful in the real world. You only need about 40 digits to calculate the circumference of the observable universe to within the size of an atom, and NASA uses only 15 digits for literal rocket science.
22/7 is a perfectly serviceable approximation for most applications. Heck, the Babylonians approximated pi as 3 and that was plenty close enough for all of their architecture.
Explain to a five year old: when you divide the circumference (the distance around the circle) by the diameter (the widest distance across it) you get three and a bit. When you do the long division on the “and a bit” there keeps being a remainder, so you have to keep adding decimal places.
We have many ways to calculate pi.
The first way was to take a circles circumference and divide it by its diameter.
Since then, we have found multiple infinite sums that result in pi. We use these infinite sums to find pi to a greater and greater level of precision.
I don’t remember the formula we use, but we only need ti calculate it out to about n=6 (six stages of the infinite sum) to get an insane level of precision. Running the infinite sum out further just gets us even closer to pi, and we dedicate a ton of computing power to this all the time.
This is the best explanation I’ve seen that answers that. From Veritasium
Latest Answers