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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:

 

Delete

 

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:

https://www.desmos.com/calculator/j9ucrkjewc

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