### 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

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 differential operator in terms of one variable into a series of differential operators in terms of othe…

### Lab Book 2014_07_10 More NaI Characterization

Summary: Much more plunking around with the NaI detector and sources today.  A Pb shield was built to eliminate cosmic ray muons as well as potassium 40 radiation from the concreted building.  The spectra are much cleaner, but still don't have the count rates or distinctive peaks that are expected.
New to the experiment?  Scroll to the bottom to see background and get caught up.
Lab Book Threshold for the QVT is currently set at -1.49 volts.  Remember to divide this by 100 to get the actual threshold voltage. A new spectrum recording the lines of all three sources, Cs 137, Co 60, and Sr 90, was started at approximately 10:55. Took data for about an hour.
Started the Cs 137 only spectrum at about 11:55 AM

Here’s the no-source background from yesterday
In comparison, here’s the 3 source spectrum from this morning.

The three source spectrum shows peak structure not exhibited by the background alone. I forgot to take scope pictures of the Cs137 run. I do however, have the printout, and…

### Unschooling Math Jams: Squaring Numbers in their own Base

Some of the most fun I have working on math with seven year-old No. 1 is discovering new things about math myself.  Last week, we discovered that square of any number in its own base is 100!  Pretty cool!  As usual we figured it out by talking rather than by writing things down, and as usual it was sheer happenstance that we figured it out at all.  Here’s how it went.

I've really been looking forward to working through multiplication ala binary numbers with seven year-old No. 1.  She kind of beat me to the punch though: in the last few weeks she's been learning her multiplication tables in base 10 on her own.  This became apparent when five year-old No. 2 decided he wanted to do some 'schoolwork' a few days back.

"I can sing that song... about the letters? all by myself now!"  2 meant the alphabet song.  His attitude towards academics is the ultimate in not retaining unnecessary facts, not even the name of the song :)

After 2 had worked his way through the so…