Quick Post

Why is it always at 12am that I am suddenly filled with the desire to do something productive?

Anyway, this is a post regarding a class of functions that are fun (subjective), of which I might make an elaborated post about after I’m done with my Analytic Number Theory post.

I’ve yet to look into this thoroughly since I only started doing so today 1150pm so here is a special case:




Yeah, does not look so impressive… YET.

Here’s the cool part: Take out your calculator (preferably a scientific one), and ensure that it is set to Radians.

Now, find “F(1)”. Did you get “F(1) = 1”?

How about “F(2)”? Did you get “F(2)=2”?

Continue to do this until “F(4)”, do you see the pattern?

What about “F(5)”? Oh? It loops back to “F(5)=1″…

How about “F(6)”? How about “F(2015)”?

So here’s it: “F(n)” outputs the remainder when “n” is divided by “4”!

So “F(2015)=3” since “2015” divided by “4” gives a remainder of “3”!


Now how did the godly Julia derive such an amazing (actually not so) function?

Sorry not going through how goodnite.

How the function looks like when graphed out:



Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s