Happy Pi Day!

For those who don't know, today is March 14, or "3.14," which is an approximation of π.  Hence Pi Day.  I know... real nerdy stuff.  But it's harmless fun, so here we are.

What are we supposed to do on Pi Day?  Good question.  Some people eat pies, or bake pies, or do other things with pies.  I don't have any pies on hand, so I won't be doing any of that.  I can do some math, though.  That'll be fun, right?  Well, no, probably not.  But we'll do it anyway.

The volume of a sphere is ​⁴⁄₃ πr​³.  (Like those fancy subscripts and superscripts?  Heh.  I had to copy and paste that stuff.  I have no idea how to properly format it in Blogger.)  Now let's take the derivative of that formula.  :o  I know, I know... Calculus!  Be still my beating heart!

First you multiply the exponent by the coefficient to get your new coefficient.  Three times four-thirds gives you four.  Then you reduce the exponent by one to get your new exponent, so it goes from three to two.  Your derivative is this:

 4πr​²

 And that just happens to be the equation that describes the surface area of a sphere.  :o 

"Wait a minute, Uncle Jeff... you're telling us that the derivative of the volume of a sphere is equal to the surface area of a sphere?"

Yes, that's what I'm telling you.  Pretty neat, huh?

"Wow.  Calculus is like sorcery."

Yep.  It's like sorcery.  Congratulations.  You're a wizard now.  :D

So that's our use of π for today.  Happy Pi Day, folks!