What is the difference between pie and 3.14

If you have a circle, you can measure two things: the distance around the perimeter of the circle circumference and the distance across the widest part of the circle diameter. No matter how big your circle, the ratio of circumference to diameter is the value of Pi. Pi is an irrational numberyou can't write it down as a non-infinite decimal. 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. Measure the circumference with a ruler. Next, measure the diameter of the circle, which is the length from any point on the circle straight through its center to another point on the opposite side.

The diameter is twice the radius, the length from any point on the circle to its center. If you divide the circumference of the circle by the diameter, you will get approximately 3. A larger circle will have a larger circumference and a larger radius, but the ratio will always be the same. If you could measure and divide perfectly, you would get 3.

Otherwise said, if you cut several pieces of string equal in length to the diameter, you will need a little more than three of them to cover the circumference of the circle.

Pi is most commonly used in certain computations regarding circles. Pi not only relates circumference and diameter. Amazingly, it also connects the diameter or radius of a circle with the area of that circle by the formula: the area is equal to pi times the radius squared.

Additionally, pi shows up often unexpectedly in many mathematical situations. For example, the sum of the infinite series.

The importance of pi has been recognized for at least 4, years. Two different graphs!!! Difference between Pi and 3. Show older comments. Vote 0. Accepted Answer: Azzi Abdelmalek. Hello i am a learner of matlab and i had a doubt. I have written a code to plot a cosine graph as followed. I have expected the same graph would be plotted for both the variables y and y1 in my code. Please help me out in this Thanks in advance!!!

Accepted Answer. Azzi Abdelmalek on 24 Sep Cancel Copy to Clipboard. We can explain this: the variation of t is.