Ok, pi is probably a bit over the head of your average 5 year old. I know the definition of pi is circumference / diameter, but is that really how we get all the digits of pi? We just get a circle, measure it and calculate? Or is there some other formula or something that we use to calculate the however many known digits of pi there are?
In: 716
One of the more basic “formula” approaches roughly goes:
– There are certain angles that have easy, exact trigonometry values. For example: sin(pi/6) = 1/2 (that is: 30 degrees)
– Because calculus, we happen to know some ways of calculating certain trig functions as an infinite sum of normal polynomial values. Inverse sin is one of them.
– From the first, if we calculate the inverse sin of 1/2, then multiply by 6, we have determined the value of pi. From the second, we can do that just with this polynomial. So, taken together, we can write down a formula where the more terms we add, the closer we get to the exact value of pi.
Proving the formula isn’t particularly simple — but you can look it up easily enough.
There are quite a few formulas like this; they tend to have varying properties in terms of how hard they are to calculate, and how quickly they reach a given accuracy.
Latest Answers