### 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

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…