IRON NODER: This Iron Noder challenge has been amazing. Thank you, Aerobe, for inspiring and leading, and for The Custodian, who got me to write that first node and break down the wall of resistance to writing I've had for so long.
It seems like a very long freight train, this list of nodes I want to write. Some are quite involved. All of the geometry nodes are interlocked, and I am finding that I can't write one without wanting to write (or improve) others.
All the while I'm writing these nodes, I'm filling out a notebook full of math formulas on geometry. It's lovely writing with a fountain pen in a book with real paper. Sketches are done in pencil and in a four color pen. Mathematics is indescribably beautiful. Formulae are beautiful. The artwork has to be beautiful too.
RUNNING: Sometimes I'll write for a few hours and then have to go running. The run is usually an hour or so. Some days I'm slow, and some days I feel like I'm moving pretty fast. The main thing to beat is boredom. I listen to podcasts for music by Tiesto, Paul Oakenfold, Armin van Buuren (techno and electronica - helps the running pace), and also podcasts by Nature magazine and NPR.
The other day I ran to Reston Town Center here in Reston, VA, and the middle of the town center was crowded with runners. I used to be self-conscious about my appearance around runners. I was noticeably heavier than everyone else. Now I look like one of them. The Fairfax County fire department was sponsoring a Nearly Naked run so that the runners could show off some skin. It was a benefit run for burn victims. The idea was that we would celebrate the skin we take for granted, when burn victims don't take their skin for granted any more. It was a great idea, and there were nearly as many onlookers as there were runners. A lot of buff firemen there. The ladies seemed to like that.
The course was only a mile. The nice thing about this race was that it was in its first year, and the organization was loose. The run was timed - a big digital clock was above the start/finish pylon. I'd wanted to time myself for a while to see if my pace, that I thought was getting faster as I was losing weight, was real, or if it was a figment of my imagination. I'd run three miles before this race, but that wasn't especially tiring. It was a good warm-up.
I deadheaded behind the runners who had actually paid money to do the race. When the race started, it only took 15 seconds to get to the start pylon. (Marathons typically have so many people that it takes an average runner four or five minutes to cross the starting line.) And then we were running.
It felt good for the first half mile, and then I sucked wind pretty badly. Everything started cramping up: thighs, shoulders, calves. Ugh. I kept thinking of my friend Lesley, who was also getting into running shape, who was posting some pretty good times - 8:30 to 8 minute miles, and I wondered if I was even in her league. (Her response: "BOO fuckin YA on the 8:30 mile!!! Sweet!!" Gotta love a chick who talks like that.)
It's kind of hard to run with a dog on the leash, but the dog kept up, and although we couldn't pass very well because she tended to run around one side of a runner while I went the other way, we did pass a few people. I wound up crossing the finish line in 8:30. Everything hurt at the end, but it was a pretty good time for me. I ran a marathon in 1999 with 12 minute miles. Ha ha ha. (Yeah, that sucks!) So this was an improvement.
I keep thinking of my ultramarathon friend Gena, who complains of having added a few pounds, but then runs a marathon without training. She seems to run at between 8 and 8 1/2 minutes/mile. And she has no trouble running with her pit bull half-breed. When she goes out for two hours, she sometimes comes home disappointed that her dog can't keep up. What a woman. Dear god. I wonder if I will ever have one tenth the endurance she has.
BONKING: Still had to run home, which was no fun. That was the closest I've ever come to truly bonking. I'd hit that hypoglycemic point and had no energy left. Got home and almost passed out until I got some lemonade down.
Went out to dinner that night, back aching and legs stiff. That was one date I maybe should have cancelled. There were a few times when I had to get up from the table, and the lightheadedness came over me until I braced against the table and could catch my breath. Then we started drinking and laughing, and everything was fine. I've never met a woman who had never gone to bars before. This is definitely a novelty.
WRITING: So here's the list of nodes I'm planning on writing. The ones I've written have little check marks by them. The nodes that are being added to the list seem to be growing faster than the rate at which the nodes are actually getting finished.
In the pipeline, coming soon: angle bisector theorem, cevian, alternate angles theorem, excircle, excenter, geometrical notation, centroid, orthocenter, Euler line, and Malfatti's Right Triangle Problem.
There's another wave of nodes that are getting written, but they need some behind-the-scenes work: the getting-huge barycentric coordinates, the follow-up trilinear coordinates that will be a piece of cake once barycentric coordinates gets finished, radical axis, radical axis for two circles, radical center of three circles (related to excenters and to the Nagel point), power of a point with respect to a circle, and then more triangle centers: Gergonne point, Nagel point, Spieker center, mittelpunkt, Symmedian point (might be a bitch, that one), de Longchamps point, Clawson point, The nine-point circle, and orthic triangle.
It's been fun re-appreciating the old master, Euclid. His brilliance is rising with every day that I learn more modern geometry. It's also been fun catching up on the current edge of modern Euclidean geometry. Mathematicians like Clark Kimberling, Paul Yiu, Alexander Bogomolny, Jim Loy, the late Steve Sigur, John Horton Conway (he seems to be everywhere in mathematics today, the Poincare of our day). Computers are having a huge impact in the way mathematicians work and 'see' geometric relationships. Java applets embedded on Web pages can help you see things in a moment that you would have spent days figuring out with pencil and paper. Software such as Geometer's Sketchpad, Cabri, and Cinderella are revolutionizing mathematics and education. (I know, I know - I haven't written these nodes yet.... soon, I promise!)
All of this may seem pointless to others, but not to me. If there's one feeling that dominates all others is that this will make me a better engineer, and will be better able to help me teach other engineers. I do a lot of work with orbital mechanics of satellites and the communications links that connect satellites and ground terminals, and link budgets are just a whole lot of geometry. I have always tried to condense down some of the more gruesome formulae to things that are elegant, that even managers can appreciate. And now it's that time of life where younger engineers want to learn the tricks, so they want to be taught these things. I think this will help them to understand concepts like slant range equations, area in view, the area of overlapping circles (coverage of multiple spacecraft for the same spot on the ground), and so on.
The business of communications links is trickier. Once the nodes for geometry are fully developed, then I can move back into the field I really know, which is communications engineering. The mathematics of modulation and coding is pretty arcane. That is one branch of mathematics that's not so pretty, not so easy to understand, and not so easy to teach others. That will be next. I'm going to see how simple I can make it. My high school buddy Jim has been pressing me for an as-simple-as-possible explanation for Claude Shannon's extremely cool 1948 papers, "A Mathematical Theory of Communication," and the companion piece, "Communication in the Presence of Noise." That will be a challenge.
THE IRON NODER CHALLENGE 4: FERRASSIC PARK
Day: 15
Nodes written: 18
- Electrical Engineering & Communications Theory
- √ Radio Direction Finding
- Geometry Series
- √ Polya's Ten Commandments for Mathematics Teachers
- √ incenter
- √ incircle
- √ circumcenter
- √ circumcircle
- √ A circle is defined by three points
Science in the news: New elements
- √ darmstadtium
- √ roentgenium
- √ copernicium
- island of stability
Geometry Series
- √ Perspector
- √ Encyclopedia of Triangle Centers
- √ Semiperimeter
- √ Menelaus
- √ Giovanni Ceva
- √ Stewart's Theorem
- Angle Bisector Theorem
- Cevian
- Geometric Notation
- Excenter
- Excircle
- centroid
- orthocenter
- Gergonne point
- Nagel point
- Euler's Line
- Trilinear Coordinates
- Barycentric Coordinates
- Alternate Angles Theorem
- Test for Collinearity
- Test for Point Inside Triangle
- Confessions of A Geometry Addict
- Triangle and Circle Geometry
- Triangle and Circle Geometry - Problem Set
- Triangle and Circle Geometry - Solution
- Steiner Ellipse
- Coordinates of the intersection of Two Lines
- Coordinates of the Intersection of a Line Fit Through a Point, and a Tangent to a Circle
- Equation of a Line Normal to a Line and a Point
- Geometer's Sketchpad
- Cabri - Interactive Geometry Software
- Cinderella - Interactive Geometry Software
- Cut the Knot
Electrical Engineering & Communications Theory
- spread spectrum
- (noise stuff)
- The kTB Noise Floor
- Link Budget for Geostationary Communications Satellites
- Link Budget for LEO Satellites
- (Shannon bound)
- (coding gain)
- Claude Shannon
- Andrew J. Viterbi
Reading
- Madame Bovary
- (Great Books reading list)
General Math Topics
- Frank Ramsey
- Ramsey Theory
- geometric mean
Chinese Space Program
Slice of Life
- √ November 6, 2011 daylog & Iron Noder progress
- √ November 15, 2011 daylog & Iron Noder progress
- (Great Books reading list)
- (Distance Running Progress)
- On being newly thin