Why pi is 22/7

Is Pi actually infinite? Can pi be squared? Can pi be solved? Is there a in pi? Are there any zeros in pi? Do any numbers repeat in pi? What is the most repeated number in pi? Where is the first 0 in pi? What are the first 3 numbers in pi? What is pi in binary? Is Googolplex bigger than infinity? What is the smallest number in the universe?

How much is a zillion? What is zillion number? Is any company worth a trillion dollars? Is Jillion a number? 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. Pi has been known for nearly 4, years and was discovered by ancient Babylonians. A tablet from somewhere between B. The ancient Egyptians were making similar discoveries, as evidenced by the Rhind Papyrus of B. In this document, the Egyptians calculated the area of a circle by a formula giving pi an approximate value of 3.

There is even a biblical verse where it appears pi was approximated:. And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. The first calculation of pi was carried out by Archimedes of Syracuse B. One of the greatest mathematicians of the world, Archimedes used the Pythagorean Theorem to find the areas of two polygons.

Archimedes approximated the area of a circle based on the area of a regular polygon inscribed within the circle and the area of a regular polygon within which the circle was circumscribed. Jones used 3.