Why does pi have infinite decimals

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Take this one, from Leonhard Euler, probably the greatest mathematician ever, in the 18th century:. And Srinivasa Ramanujan, a self-taught mathematical genius from India, discovered the totally surprising and bizarre equation below in the early s. Each additional term in this sum adds eight correct digits to an estimate of pi:.

Much like with the search for large prime numbers , computers blasted this pi-digit search out of Earth orbit and into deep space starting in the mids. But maybe 22 trillion digits is just a bit of overkill. No, you can't just plug it into your calculator and get Pithat assumes you already know Pi. Instead, we need to do a Taylor Series expansion of the inverse tangent. The basic idea behind the Taylor Series is that any function sort of looks like a power series if you just focus on one part of that function.

Using this, I can represent the inverse tangent of some value x as an infinite series:. That's it. Now you can just plug away at this formula for as long as you likeor you could have a computer do it. Here is a program that calculates the first 10, terms in the series just press play to run it :.

View Iframe URL. See, that's not so difficult for a computer. However, you can see that even after 10, terms the calculated value is still different than the accepted value. This isn't the best series to calculate Pibut I said that earlier. This is my favorite Pi activity. Here is the idea. Generate pairs of random numbers between 0 and 1 to create random x,y coordinates. Plot these points on a 1 by 1 grid and calculate their distance to the origin.

Some of these will have a origin distance less than 1 and some will be greater than 1. The points with a distance of less than one are "inside a circle"actually it's a quarter of a circle. You really should play around with this because it's fun. Try changing the number of points or something like that. I included a "rate " statement so you can see the points being added.

These rational expressions are only accurate to a couple of decimal places. While there is no exact value of pi, many mathematicians and math fans are interested in calculating pi to as many digits as possible. The Guinness World Record for reciting the most digits of pi belongs to Rajveer Meenaof India, who recited pi to 70, decimal places while blindfolded in Meanwhile, some computer programmers have calculated the value of pi to more than 22 trillion digits.

The website piday. Pi has been known for nearly 4, years and was discovered by ancient Babylonians. A tablet from somewhere between B.