Calculating the distance between two points with the Pythagorean Theorem

So, before we get started, I need to define some things.
Right Triangle:
A right triangle is a triangle with a right angle.
220px-Triangle.Right.svg
Pythagorean Theorem
The Pythagorean Theorem says that .  and  are the two shorter sides of the right triangle. The long side is called the hypotenuse. From now on we will refer to as . If we want to get , instead of , we can do 

Pythagorean-Theorem

Ok. Now that we’re done with that, we can start actually calculating distance. This part is pretty simple. Imagine we have a cat that wants to get to a mouse, but needs to know how far away it is. The cat is at 0,0, and the mouse is at 5,5. Let’s call the cat’s x and y “cx” and “cy” , and let’s call the mouse’s x and y “mx” and “my”.In many of these equations, I will be using a lot. If a number is between those bars, it means that it will be made positive (). First, we find , and we find . These are the differences between the x values and the y values. Now we take those numbers (let’s call them “dx” and “dy”). To get , we do . Now we can do . We are done.  is our distance. This seems long, but we just produced a short formula to find distance. Here is the completed formula: 
For those of you still having trouble, this might help explain why you can’t just add dx and dy, and why you are using right triangles:
ptfindingdistances

On-The-Fly Code Injection (Inserting Header and Footer)

Recently, I added a feature to my website that allowed me to inject code into my site. Currently all pages in my site have this code injected into them. It adds my favicon, LaTeX, Markdown, and an emoji tag I created. I had a lot of trouble finding this, so I will show you my code. Maybe someone will want it.
Htaccess:

RewriteEngine On
RewriteRule ^head_foot.php$ - [L]
RewriteCond %{REQUEST_FILENAME} -f
RewriteCond %{REQUEST_URI} !^/joke/ #Exclude scripts that generate images. This will corrupt them.
RewriteRule \.(php|htm|html)$ /head_foot.php [E=FILE:%{SCRIPT_FILENAME},L]

head_foot.php:

<?php
include("header.html"); #Add Header
#Now get webpage:
include getenv('REDIRECT_FILE');
?>