## Introduction

In the previous post about my monitor, I used five colors: red, green, blue, white, and a pale purple. For each of them, I began by specifying RGB values… I used Digital color meter to find their XYZ values… and I demonstrated that the relationship was nonlinear when applied to the purple color.

The relationship was…

XYZ = M (RGB)^1.801

where M, however, is linear (a matrix).

I found the nonlinear part of the relationship from the following graph out of my ColorSync utility…

## Happenings – 2010 June 26

It’s not yet 9 AM as I begin to write this… I’ll do this first, and then turn my inner child loose… he wants to do control theory… and we may not stop after I start. (I did a little reading in control theory yesterday, and this morning the kid wants to do some computing with it.)

Well, we’ll have to stop at some point… I really want to get a technical post ready today for posting Monday evening.

Not a whole lot has happened since the last Happenings post.

I made good progress in Brown’s “Boolean Reasoning”, both understanding the math and getting Mathematica to do things for me… but I’ve stopped at a chapter boundary.

One of Brown’s major references has arrived: a used copy of Rudeanu’s “Boolean Functions and Equations” (North-Holland, American Elsevier, 1974). It looks wonderful – not just because it’s full of examples, but because it’s pretty clearly written.

This means I have two books dedicated to the subject of Boolean equations, and a third book which includes the topic. Even better, the three have different approaches. (The third one is the Schaum’s Outline, “Boolean Algebra & Switching Circuits” by Mendelson.

Incidentally, two of the three are quite cheap, since Brown’s book is a Dover paperback.

And I think that’s it. I want to do some computing this morning, and I just don’t have the patience… I’m just not mellow enough… to chatter about my mathematical life. Not this morning. I need a math fix.

## introduction & setup

I want to play with five colors. Four of them are perfectly straight-forward: red, green, blue, and white. The fifth color, looking purple to me, is close to one of the colors on the Gretag Macbeth color checker; we’ll be seeing this color again in a subsequent post.

I have two software tools which came with my Mac: the DigitalColor Meter and the ColorSync Utility. If you are not on a Mac, perhaps you have, or can get, something similar.

I want to know the relationship between RGB and XYZ on my monitor. First I will establish that the relationship is not linear; then I will show how what it is and how I found it.

Let’s try finding a linear relationship by looking at the relationship between RGB and XYZ for my five chosen colors, but especially for red, green, and blue.

Here is a red disk, defined by RGB = (1,0,0). If you’re new to my blog, the following commands are Mathematica®.

## Happenings – 2010 June 19

Mathematically speaking, my life is fairly straightforward this weekend (famous last words).

My kid has worked on “Boolean Reasoning” (Frank Markham Brown, Dover) this morning. When I stopped, I think we had just figured out how to find the “consensus” of two logical products. Oh, I know how to do it by hand – the challenge is to get Mathematica® to do it.

What’s that mean?

If, for example, I have two logical products (using juxtaposition for conjunction, i.e. for “and”)

x y z’ , x w z,

their consensus is found by taking their conjunction…

x y z’ x w z,
Read the rest of this entry »

## Orbits: the elliptical orbit

I want to show you the geometry of an elliptical orbit.

Most of this post is reference, but note that it includes a calculation of the Hohmann transfer orbit between two circular orbits.

Let me start with a simple drawing:

We measure the angle $\nu\$ from the horizontal, counterclockwise. All our training in trigonometry says we should label the horizontal line as the x-axis — and I will subsequently do so, but it’s not essential.
Read the rest of this entry »

## Happenings – 2010 June 12

As I begin this draft, I am hoping to talk about the joy I take in mathematics, my sense of wonder, and something called “beginner’s mind”. We’ll see how it goes.

But first let me just talk about what’s been happening.

Once again, no posts went out last weekend. This time I had a different excuse.

Saturday morning, when I should have been drafting a happenings post, I discovered that I needed a mathematics fix. Never mind what I was supposed to do, I needed to do some mathematics. So I did.

I spent all of last Saturday and half of Sunday looking at regression (OLS, ordinary least squares). Finally, Sunday afternoon I returned to orbital mechanics. But that didn’t give me enough time to finish off a technical post.

As for the blog itself, sometime in the afternoon of June 10, one of the color posts (the CIE chromaticity chart) surpassed my only Fourier analysis post, moving into second place all-time.
Read the rest of this entry »