The Merry Christmas Equation

This is a fun post for the holiday season that I first read over at my friend Guillermo’s page, Math and Multimedia. You often hear that everything can be described by mathematics. In this case, we’re going to use some math to convey a special message for this time of year!

To begin, let’s start with this equation:
Now let’s rearrange a bit by multiplying both sides by r2:

We currently have in this expression a natural logarithm. Since the natural logarithm ln(x) is defined as the inverse function of the exponential function ex, we can remove the logarithm from our equation entirely by raising the number e to the power of our equation:

Now, since ln(ex) is equal to x, we can apply this to our equation to leave only what was in the parentheses on the right side:

To remove the denominator, we have to multiply both sides by m:

Finally, with a little bit more rearranging, we are left with our final expression:

Merry Christmas and Happy Holidays to all of my readers, and best wishes for the New Year!