Why do we use 3.14 for pi

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Click the link to confirm your subscription and begin receiving our newsletters. This means you need an approximate value for Pi. The simplest approximation for Pi is just 3. Yes, we all know that's incorrect, but it can at least get you started if you want to do something with circles. The early history of mathematics covers many approximations of the value of Pi. The most common method would be to construct a many-sided polygon and use this to calculate the perimeter and diameter as an estimate for Pi.

Other cultures found ways to write Pi as an infinite seriesbut without a computer, this can be sort of difficult to calculate out very far. There are many methods to calculate Pi but I will go over the simplest to understand. It starts with the inverse tangent function. 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. You can find Pi in nature, too. For example, you can find it in the pupil of our eyes or ringed splashes in ponds. Albert Einstein even found Pi in the shapes of rivers. OK, he was born in , not Got a science question? E-mail Dr. Wendy Sue Universe at Dr. Universe wsu. Ask Dr. Universe is a science-education project from Washington State University.

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