Now, if you’re like me, your eyes are probably glazing over right now because these concepts sound super boring and complicated. But trust me when I say that they’re actually pretty cool once you get past all the jargon!

Before anything else what exactly is a continued fraction? Well, it’s basically just a fancy way of writing down a number as an infinite series of smaller numbers. For example, let’s take the number pi (π) and write it out in its simplest form:

π = 3 + 1/7

Now, if we want to make this into a continued fraction, all we have to do is keep breaking down each term until we get something that looks like this:

π = [3; 7]

That’s right the square brackets indicate that we’re dealing with a continued fraction. And what does that mean? Well, it means that pi can be expressed as an infinite series of smaller numbers (in this case, 3 and 1/7) that keep getting closer and closer to its true value.

But why is this important? Why should we care about something like a continued fraction when there are so many other ways to write down a number? Well, for one thing, it can be used to calculate the values of certain functions (like the gamma function) with incredible accuracy. And for another thing…well, let’s just say that it looks really cool on paper!

Now, onto our second topic the gamma function. This is a mathematical concept that allows us to calculate the factorial of large numbers without having to do all those ***** multiplications by hand. For example, if we want to find out what 10! (which stands for 10 factorial) looks like, we can use the gamma function to get an approximation:

Γ(n+1) = n!

So, in this case, we would plug in n=10 and solve for x:

Γ(11) = 10!

And voila we’ve got our answer! But why is the gamma function so important? Well, it has a ton of practical applications (like calculating probabilities or solving differential equations), but more importantly…it looks really cool on paper too!

Two of the most fascinating topics in mathematics that will make your eyes glaze over with boredom if we talk about them for too long. But hey, at least they look pretty when you write them down!