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### Samothraki: Day 3

Day 1 Day 2

The third day in Samothraki, I took off on a tour around the Eastern edge of the island. The variety of sights within a small space is stunning. I visited an ancient temple site overlooking the ocean, hiked in the mountains to an idyllic, deserted waterfall, and wondered around a black pebbled beach!

I've written previously about the The Temple of the Great Gods, so I won't add too much. The site is amazingly well preserved considering that Alexander the Great's parents met here. The statue of 'Winged Victory' that is now on display at the Louvre was found here. By the way, France and England, the folks in Greece would like their stuff back.

A short ride from the temple and into the hills behind Θερμα, brings you into a dense forest on the mountainside. You can hike back in to a series of waterfalls. I only went up to the first one. In the off-season, the area was completely deserted except for a few goats.

A ride east and then south along the eastern coast brought me to a warm beach covered in black pebbles that rolled in and out with the tide.

### 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…

### The Javascript Google URL Shortener Client API

I was working with the Google API Javascript Client this week to shorten the URLs of Google static maps generated by my ham radio QSL mapper. The client interface provided by Google is very useful. It took me a while to work through some of the less clear documentation, so I thought I'd add a few notes that would have helped me here. First, you only need to authenticate your application to the url shortener application if you want to track statistics on your shortened urls. If you just want the shortened URL, you don't need to worry about this. The worst part for me was that the smaple code only showed how to get a long url from an already shortened rul. If you follow the doucmentaiotn on the insert method, (the method for getting a shortened url from a long one), there is a reference to a rather nebulous Url resource required argument. It's not at all clear how to create one of these in Javascript. The following example code shows how:
var request = gapi.clie…