+349 WARNING: What you are about to read contains circles of all shapes and sizes, as well as pies that when consumed, has a side effect of increased mathematical knowledge. If you are not ready for this, order a pizza pie instead.
Hello, guys and gals. I posted this for you guys to learn about pi, that circlular constant that can be a bit confusing at times. So, yeah. Let's get started on this literally infinite numerical journey. Aaaaand, I hope you read the warning above, because pizza is good.
1. What is PI?
Pi is the ratio between the diameter and the circumference of a circle. The interesting thing is that it is the same for all circles, whether it is as big as a planet or as small as an atomic nucleus.
Let's say the diameter of a circle is 2.773. We know that the circumference of a circle is equal to:\({\Pi}d\)
So, let's compute. 2.773 times the estimate of pi, 3.1416. This is equal to 8.7116568.
Now let's divide the circumference by the diameter: \(\frac{8.7116568}{2.773}=3.1416\)
So now we can say that the ratio of C to d is 3.1415:1.
Here is another demonstration of pi:
If you get the diameter of a circle and stretch it around the circumference, you would see that you could fit 3 and a part of the diameter. That part is the decimal of pi: .141592...
Oh, and it's also an irrational number.
2. Importance of PI
Now that we know what this troubling constant is, now we ask, what is it for? What is it's significance in mathematics? Well, I'll give you some examples:
2.1.) Circumference of a circle: \(\Pi d \)
2.2.) Area of a circle: \(\Pi r^2\)
2.3.) Gregory-Leibniz series: \(\frac{\Pi}{4}=1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}...\)
2.4.) An unproven infinite series by Srinivasa Ramanujan: \(\frac{1}{\Pi}=\frac{2\sqrt{2}}{9801}\sum_{k=0}^{∞}\frac{(4k)!(1103+26390k)}{(k!)^4396^{4k}}\)
And more...
Source: http://www.geglobalresearch.com/blog/what-is-significance-of-pi-in-mathematics
3. Math Challenge
Now, let's test your mathematical knowledge about circles, shall we? Aproximate pi to 3.14.
3.1.) If the diameter of a circle is 3cm, what is it's area?
3.2.) If the area of a circle is 452.16, what is it's circumference?
3.3.) What is the radius of a circle who's area is equal to it's circumference?
Post your answers in the answers section.
4. Bonus Section
Of course, this HAS to have a bonus section. So I decided to put 100000 digits of pi. Yeah:
http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html
So anyway, that's it for today. Thanks for reading 
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(Are they all gone? Phew, that was a mouthful. I'm glad it's over.)
