*did*get a round Tuit. (Even if I had to design and render it myself.)

# Tag Archives: 3D

## A Round Tuit

## Vectors and Scalars (oh, my!)

Put on your arithmetic caps, dear readers. Also your math mittens, geometry galoshes and cosine coats. Today we’re venturing after numeric prey that lurks down among the lines and angles.

There’s no danger, at least not to life or limb, but I can’t promise some ideas won’t take root in your brain. There’s a very real danger of learning something when you venture into dark territory such as this. Even the strongest sometimes succumb, so hang on to your hats (and galoshes and mittens and coats and brains).

Today we’re going after *vectors* and *scalars* (and some other game)!

## SR #18: Light Cones

Last time I focused on how it was possible for Al to see — even enclose in a tunnel — a train that appears shorter to him due to its motion. It turns out that the train Al sees is a stack of time slices of the train at different moments. As we’ve seen, lots of things look different in a moving frame.

Today I want to say a little about Em’s point of view, run some numbers, and take you through a little math (just one equation, I promise). Then, because it’s Friday (when I try to write about light), I’ll introduce you to light cones.

They’re not actually necessary, but they’re kinda cool.

## SR #13: Coordinate Systems

The main topic this week was how simultaneity is relative to your *frame of reference*. How there are (virtual) *lines of simultaneity* where all points on some line — at all distances from you — share the same moment in time. For any instant you pick, that instant — that snapshot — includes all points in your space.

A line of simultaneity freezes the relative positions of objects at a given moment — which enables distance measurements. Simple example: When their watches both read 12 noon, Al and Em were 30 miles apart. A more mathematical example uses ** x**,

**, &**

*y***(&**

*z***), but it amounts to the same thing: a**

*t**coordinate system*.

The gotcha is that simultaneity and coordinate systems *are relative* when motion is involved!

## SR #9a: Extra Diagrams

A couple of readers have asked about the diagrams in this series of Special Relativity posts. I created them with the freeware 3D ray tracing application, POV-Ray. The diagrams are actually three-dimensional “scenes” designed to be viewed as flat pieces. If some of the “dots” look more like little spheres, that’s because they are!

I wrote some introductory posts a while ago (here, here, and here). You can read those if you want more details about the application.

For a little (optional!) Friday fun, I thought I’d share some POV-Ray images that have a bit more “dimension” to them.

## SR #6: More Diagrams

Last time I introduced you to the idea of a *time-space diagram*, which is a kind of map used to describe motion. As with many maps and diagrams, we choose to use a flat, two-dimensional representation. Someday hologram technology may advance to casual use of three-dimensional images, but so long as we use paper and display screens, we’re stuck with two.

Motion is movement in both space *and* time, so we want to use one of our two dimensions to represent time. That leaves us with only one remaining dimension for space, so our diagrams exist in a reduced one-dimensional world.

Today I’ll explore that world in more detail.

## SR #5: Diagrams!

Last week I introduced you to the idea of *relative motion* between *frames of reference*. We’ve explored this form of relativity scientifically since Galileo, and it bears his name: *Galilean Relativity* (or Invariance). Moving objects within a (relatively) moving frame move differently according to those outside that frame.

I also introduced you to the idea that light doesn’t follow that rule; that light moves the same way to all observers. This is what makes Special Relativity different. It turns out that, if a frame is (relatively) moving fast enough, some bizarre things happen.

*Time-space diagrams* will help us explore that.

## Boldly Going

As reported earlier, this week got off to a rough start. I let my guard down (foolishly) and got nabbed by the greedy PC rapists. All I wanted was to find a particular font for a project. The next day a more careful search turned up exactly what I needed, the fonts and just the fonts (ma’am).

Monday I mentioned that I planned to share my font-needing project with you. It’s not finished (many of my projects live a long time as I tweak them — some are living things that grow and improve *forever*). But it turned out so much better than I expected, I just had to share it with you this Science Fiction Saturday.

I’m also going to boldly try a new WordPress blogging trick!

## Dimensional Coordinates

The maps you find in some buildings and malls have a little marker flag that says, “You are here!” The marker connects the physical reality of where you are standing at that moment with a specific point on a little flat map.

Your GPS device provides your current location in terms of *longitude* and *latitude*. Those numbers link your physical location with a specific point on *any* globe or map of the Earth.

But to *fully* represent our location, longitude and latitude are not quite enough. (We might be high overhead in a hot air balloon!) To fully represent our position, we need a little more ‘tude, but in this case that’s *altitude*, not attitude.

We need three (and only three) *coordinates* to completely represent our location in space. This post is about why.