### Samothraki: Day 2

Back on Samothraki:

Notes on the slide show are included below.

The pictures shown were taken in early September. The island is beautiful then. Most of the tourists have gone home and there's just a slight chill to the air in the mornings.

Day two starts in Kamariotissa. The picture shows the main street of the little port town. At Mike's car and bike rentals you can rent a scooter, a motorcycle, a car, or sometimes even a house. I lucked out and got everything I needed in one stop!

There's a great internet cafe next to a coffee shop if you need to send messages home, or upload photos. The cafe is shown in the lower right-hand corner of this photo.

This is all you need to get around to get around Samothraki! There's not a whole lot of traffic on the roads. Even on the rougher roads in the country, a scooter does just fine. Make sure you learn how to use the kick starter as well as the electronic ignition, the knowledge will come in handy. Also, keep in mind that the only gas station is located in Kamariotissa, so fill up before heading out.

The first full day, I rode up to capital city of Χορασ. The ride is easy and only takes about thirty minutes. The city is nestled into the hills of the island. It can actually be seen from the ferry on the ride to Samothraki. The remaining slide show photos are of Χορασ.

The Locations:

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

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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…