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### History, Ham Radio, and Touch

My dad and both of my grandfathers are masons. Consequently, as a kid, I could always find a copy of Albert Pike's, "Morals and Dogma", or a lodge monitor, full of geometric diagrams, on the bookshelf. My dad and I would talk about geometry problems like Euclid's 47th problem, the Pythagorean Theorem. Dad told a story that Euclid had proposed this problem to his student Pythagoras by sketching it in the sand while walking along the beach. Then, by drawing out a right triangle and making squares of the sides, Dd would show that the squares in the Pythagorean formula had geometric as well as mathematical meaning. The areas of squares made from the short legs of the triangle will add up to the area of the square made from the long leg of the triangle. Geometry presented as a story instead of a dry rigorous science is what held my interest as a kid and is what has piqued my recent interest in the new series "Touch" and "Daybreak" with their references to 'Sacred Geometry' and Platonic solids.

In the case of "Touch", the happy coincidences theme has also struck a chord. On his way to the Philipines to serve in the Army Signal Corps in 1960's, my dad was bumped from three separate flights that were supposed to take him to the island base. He finally had to hop a ride on a Naval ship. He found out later that all three planes had gone down over the Pacific.

My dad developed an interest in radios while in the Signal Corp that was a big part of my childhood as well. One afternoon, my dad turned up with two of his buddies and a giant radio that took two of them to lift onto the tabletop. It was covered with dials and full of gears and mechanized plungers and glowing vacuum tubes. My dad intended to become a ham radio operator. He's still not licensed, but I was hooked, and a mere twenty years later got my license. I work kind of slowly sometimes.

So, I was intrigued to say the least when episode 8 of Touch opened with a vacuum tube falling onto the floor of an MTA bus from what later turned out to be a ham radio. This ham radio would go on to be pivotal in the efforts to save the life of an Italian astronaut. The astronaut in question happened to have an experimental comm system designed by his engineer wife. In case your wondering if ham radio can really be used to speak with the International Space Station, the answer is yes! Here's a video of ham radio operators and high school students speaking with astronauts on the ISS.

### 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…