A Gift for the Upcoming Birthday Bash

As a rule, men are notorious last-minute shoppers. One of my sisters goes to gem shows, picks up tons of inexpensive but tasteful jewelry and sells it off, as last-minute Christmas gifts to her male friends.

How can software compete? Well, not only are Ubuntu CDs free, there's an Ubuntu-based distro for everybody.

Shopping on a budget for geeks? Your problems are over.

Grow Your Own Chistmas Gifts

Too cold in Colorado, I expect. I wonder if these grow in Oregon. Are you listening, Nan?

innovative Democrat policies

A put-up job, but still funny.

Wikipe-CD -ia

Educational articles for schools collected from Wikipedia, on a CD.

The Writings of Mark Twain [pseud.]: A Tale - Google Book Search

Lyn Mead thinks it's interesting that you can't tell what someone who's reading an eBook is reading. There's no jacket.

Yup. I never thought about it, but it is fun to walk by and look at what folks are reading.

The link is to Google's entry into the field.

Ars Longa, Vita Brevis

Art Face Off

Captain Picard's ABCs

The Star-Trek Alphabet Song.

Birthday present #2

We're sitting at a table, next to a giant pile of pennies. We play a game.

First, you put a penny on the table. Anywhere's fine, but it can't stick out over the edge.

Next, I put one on, somewhere else. I can, if I want, even touch your penny with mine, but they can't overlap.

We keep doing this until there's no place to put another penny. Last person to be able to put a penny down, wins.

What's a winning strategy, and who's the winner?

Blab school

BA grew up in a little town in rural California. His father taught high-school math. One day, his father found himself substitute-teaching the geometry class for the nearby, more affluent town.

Trying to see what the kids knew, so he'd know where to start, his dad asked them if they knew how to find the area of a triangle. "One-half the base times the height," the class said, in unison.

It sounded too much like blab school. He thought for a second, went to the board, and drew a triangle, upside down, resting on its apex. "Okay, what's the area?" he asked.

Yep. "Zero."

Birthday present

Here's the first of a pair of birthday presents for BA, the Marine Corps, and all you other Scorpios, both courtesy of George Polya. The second comes in a following post.

First, a proof of the Pythagorean theorem that I'd never seen before:

(1) Instead of drawing squares on the sides of the triangle, draw regular hexagons.

(2) Even though the area of the hexagon isn't the square of the side, it's proportional to it. A = kS².

If this is obvious, fine. If not, try drawing radii, in your mind, for the hexagon, and consider what happens to the areas of the six triangles as you grow the hexagon in your mind: double the side, quadruple the areas.

From this, you can conclude that if the Pythagorean theorem, c² = a² + b², is true then so is another flavor of the same thing: the hexagon on the hypotenuse is equal to the sum of the hexagons on the other two sides.

kc² = ka² +kb²

(3) This same argument holds for any similar polygons, regular or irregular. (After all, you can decompose any polygon into triangles.) The Pythagorean theorem is just a special case.

(4) Run the argument in step (2) backwards. If you can prove an analogue of the Pythagorean theorem for some kind of polygon, the general theorem in (3) follows, and the Pythagorean theorem is also proved.

(5) Imagine a right triangle. Flip it around so it rests on its hypotenuse, and the vertex of the other two sides is sticking way up in the air. Drop a line down from that vertex, to meet the hypotenuse at a nice, right angle. (The base of the triangle is now the hypotenuse, and the line you drew is the altitude.)

The two new little triangles you just created are each similar to the original triangle (same angles) and to one another. They sum to the whole area.

Quod erat demonstrandum.

Map/telephony mashup

I recognize that on-line maps are way cool, though they don't really get me excited. Telephony, in contrast, I get. Google -- smarter than I -- gets both.

Color vision

Dang. This actually works.

I thought it was a trick.

Secretary of Defense

Who else would you turn to for martial arts expertise?

A Sketchbook of One

Alan Haemer would be smiling at this.

My father, while an Air Force Colonel, taught painting and drawing classes, in his spare time, at night, to servicemen.

Often, the classes were University of Maryland extension courses.

After he retired, he went back to school, got an M.F.A. on the GI Bill, and taught painting and drawing at the University of Oregon.