### Ham Radio Exams are Back Online

Sometimes intersecting interests are the ones that get you moving:  How homeschooling saved the radio star!

This blog clearly started out as more of a ham radio site.  There are a variety of indicators.  My call sign's in the masthead, The logo by Dash The DogFaced Ham includes a picture I took of an old Westinghouse gauge I found in the basement of the New Yorker while I was setting up a special even station to raise awareness for the restoration of Tesla's last laboratory, Wardenclyffe.  By the way, the logo and masthead will probably change soon to reflect the blog's new focus: unschooling, but I'm getting ahead of myself.

Life is full of variety though, and so as the years progressed, the blog focused more on physics as I made my soiree into and then back out of a PhD physics program.  Recently, the blog has changed focus again, and contains posts on my new favorite thing to write about homeschooling, and more specifically, unschooling.  In the meantime, the ham radio practice exams that use to live here in the blog, and that have since relocated to http://copaseticflows.appspot.com/hamtest stopped working.  Busy with many, many other things I haven't made the time to fix them, but then my interests happened to intersect.  A homeschooling family contacted me to let me know they were studying for their ham radio exams, and would love to use the practice exams that are linked from a homeschooling blog they read, namely mine.

Here we are a few days later, and good news!  The practice exams are back up and running!  Have fun with them, and please let me know if anything can be improved.

### Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

Now available as a Kindle ebook for 99 cents! Get a spiffy ebook, and fund more physics
The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differe…

### Division: Distributing the Work

Our unschooling math comes in bits and pieces.  The oldest kid here, seven year-old No. 1 loves math problems, so math moves along pretty fast for her.  Here’s how she arrived at the distributive property recently.  Tldr; it came about only because she needed it.
“Give me a math problem!” No. 1 asked Mom-person.

“OK, what’s 18 divided by 2?  But, you’re going to have to do it as you walk.  You and Dad need to head out.”

And so, No. 1 and I found ourselves headed out on our mini-adventure with a new math problem to discuss.

One looked at the ceiling of the library lost in thought as we walked.  She glanced down at her fingers for a moment.  “Is it six?”

“I don’t know, let’s see,” I hedged.  “What’s two times six?  Is it eighteen?”

One looked at me hopefully heading back into her mental math.

I needed to visit the restroom before we left, so I hurried her calculation along.  “What’s two times five?”

I got a grin, and another look indicating she was thinking about that one.

I flashed eac…