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## This Pi Day, Calculate the Value of Pi for Yourself

It is once again Pi Day (March 14which is like the first digits of pi: 3 and 14). Before getting into this year's celebration of pi, let me just summarize some of the most important things about this awesome number.

But today, I am going to calculate pi with a numerical integral. What does that even mean? Let me start with an examplehow do you find the area of a half-circle?

The area of a circle is pi times the radius squared. This is half of a circle with a radius of 1 (no units) such that it would have an area of pi/2. If I find the area with some other method, I can just multiply this area by 2 and get pi. That's the plan.

But how do you find the area of some shapeor any shape for that matter? This is where calculus comes in handy. I can find the area of the half circle by adding up the area of a bunch of rectangles. It turns out that it's pretty easy to find the area of a rectangle. Let me just draw a few rectangles in that half-circle so you can see what I mean.

The area of each of these skinny rectangles can be found with the formula "base times height." A rectangle has a height of "y" and a base of "dx" where the dx is just some arbitrary length along the x-axis. I can find the actual value of the height because the top of the rectangle hits the circle where this height can be found from the equation of a circle.

Now I just need to add up all these rectanglesboom, that's the area of half a circle. I can write this as a sum of areas like this:

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