### When is a Rock Just a Rock?

With more pictures coming in from the Mars rover missions that 'look like something', it seems that believers are becoming ever more hopeful while skeptics are becoming ever more skeptical. In the interest of promoting open-mindedness in scientific investigations, the following Earth-bound, Mars and Mercury rocks are presented for your consideration.

 From Just a Rock More Than A Rock ??? Earth Camel Rock near Tesuque Pueble, NMImage credit The Treasury: Petra, Jordan Mars Actually, this is a special rock. The rock in the lower right foreground is thought to be an iron meteor.Image credit Maritian meteor containing fossilized bacteria?Image credit Lady on MarsImage credit Earth Bear in a Rock: Pecos River Valley, NMImage credit Mars Skull RockImage credit Mercury Spider scar: MercuryImage credit Not a rock! Also, not from Mercury.Image credit

Anonymous said…
Hi Hamilton, thank you for coming across my site! Glad to find a fellow fan (though, make that a new fan for me!) out there!

Have a great rest of the weekend!

jebbica@gmail.com

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

Now available as a Kindle ebook for 99 cents! Get a spiffy ebook, and fund more physics
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…