### Satellites, DeSTEMber, and Ham Radio

Continuing the DeSTEMber list of reasons ham radio might be cool for kids...

Satellites

Any ham radio operator can use amateur radio satellites to communicate with other hams.  There are lots of amateur radio satellites in orbit that pass over the United States every day.  Look at the picture below of the amateur radio satellites that will be radio visible over Austin, TX in the three hours after I wrote this post.

Each yellow 'wall' is the path of a satellite.  The height of each wall indicates the altitude of the satellite.

Besides the fact that it's just cool to use satellites, why would you want to use a satellite to communicate?  The small handheld radios used by hams operate at high frequencies in the range of 100 to 1000 or so MHz, (your FM radio listens to signals around 90 MHz).  At these frequencies, the radio waves move mostly in straight lines and don't bounce off the atmosphere.  So, if you want to talk to your buddy who lives over the horizon, you're out of luck, unless your antenna happens to be located in space!  You can make a line of sight contact to the satellite overhead, because it's so much higher than you are, the satellite can 'see' other radio stations that are behind your horizon and re-transmit your signal to them.

Here's a far more complete article about amateur radio satellites written by Diana Eng, Project Runway contestant, fashion designer, and ham radio operator.

### 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…

### The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though!

Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very simpl…

### 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…