IRON NODER: Maintaining a continued willingness in participating in the Iron Noder challenge has been challenged by Everything2 server hardware problems. I've voiced my frustrations in a previous daylog.
What is particularly ironic (erm) is that the Iron Noder happened at just the right time for many writers here, who have had a need to pour out pent up words. That the dam bursting is coming at just the right time is partly due to Aerobe's adroit timing, but it's also a matter of the onset of winter. We feel the chill coming, and we want to hunker down and write. Such is the case with me. My list of nodeshells is growing faster than my ability to write them.
No one can doubt Aerobe's finesse with which she's handling the Iron Noder. (PBUH). It takes courage not to be discouraged. My esteem for our new overlord grows daily.
My writing production has slowed, because some of the geometry series require real research. Today I'm heading over to the storage unit to attempt to dig out the ten or so textbooks that will help finish the series.
Modern geometry is amazing. The contrast is huge between high school memories and the present day mathematics of classical Euclidean geometry, as true mathematicians would say. We learned a love of proofs in high school: the angle-side-angle (ASA) theorem, Pythagoras' theorem, congruences, and theorems dealing with circles and bisectors and so forth. The marvelousness was in the method, not actually in what we learned. Geometry wasn't really useful to a working engineer or scientist, but its methods were. If geometry is measured by its efficacy, then it was 100% effective with me: I fell in love with mathematics in Mister Rubell's geometry class in Rocky River, Ohio.
Geometry was revitalized by a Canadian mathematician, H.S.M. Coxeter, about whom I cannot say enough, except that his mathematics is beautiful and elegant. Although Euclid, Archimedes, Apollonius, Ptolemy and their ilk of ancients were marvelous mathematicians, it's somewhat surprising at how much they didn't discover. We're discovering it nowadays. In a real sense, there have been huge breakthroughs in the last fifty years on simple things involving just triangles and circles.
Even more amazing is the use of computers in geometry research. Programs such as Geometer's Sketchpad, Cabri, Cinderella, and the awesome professional (and free!) applications such as Z.u.L. (the German version, "Zirkel und Linie" of C.a.R. - Compass and Ruler) are useful in diagramming and even researching new theorems. At the most professional levels are sophisticated mathematical tools that determine such things as triangle centers and other facts. There are about 3500 known triangle centers, and thousands of geometrical theorems and lemmas in geometry databases. Determining whether a new theorem is in fact already an existing, and known, theorem, is something that computers are becoming good at. Somewhat more interesting, computers are beginning to generate new theorems algorithmically. Some day I hope to write more about this, but for now I only have time to cover the basics of findings I've stumbled across in this last two months of my own research on the topic.
It's been a surprise to hear the reaction to my notebook of mathematics. It's full of diagrams and formulae, theorems and so forth, and I posted one or two photos of the notebook's contents on my homenode. Many of you must keep similar notebooks full of ideas and drawings, because your reaction was visceral. I think you were delighted to find similar kindred spirits out there.
WRITING: The geometry articles are proceeding painfully slowly. I'm trying to finish off excircle, but the more work I do, the more interesting facts I am uncovering. It's going to be a case where this node doesn't get finished so much as it is abandoned, as the French poet Paul Valéry said about poetry. Ditto barycentric coordinates. I understand how to go from barycentric coordinates to finding a point in cartesian coordinates, but I can't yet do the inverse: given a point's (x,y) coordinates, find the barycentric coordinates. I mean, I can, I just don't understand the why. And therefore i can't finish the node.
After these two are done, a bunch more can be released. Such nodes as centroid, orthocenter, Nagel point, Gergonne point, Euler line, mittenpunkt, Spieker center, the famous nine-point circle, and Fermat's point will be almost trivial to finish. Then there are the medium difficulty writeups, like Geometer's Sketchpad, C.a.R., phased array (a suggestion kicked off by The Custodian, and not a geometry writeup), Triangle and Circle Geometry Problem Set, which are lengthy but not taxing.
More difficult are the harder ones, like contact triangle, orthic triangle, median triangle, pedal triangle, Bevan point, Schiffler point, extangent triangle, and the problem of Apollonius. The ones I really fear, though, are the isotomic conjugate and isogonal conjugate writeups. They are essential, because they show some of the real beauty in geometry - the hidden symmetries that will delight and surprise you - but conveying this is not easy. Simpler is better. Less is more. I keep Mies van der Rohe's maxim on my lips at all times, but I fear that wordiness is a curse for me. I can't say something is beautiful - it must emerge by itself from the mathematical facts - and the beauty must be something you see. I can't force you to fall in love with a theorem. Your reactions may not be exactly like mine. And I fear ugliness in writing.
THE IRON NODER CHALLENGE 4: FERRASSIC PARK
Nodes written: 29
- Electrical Engineering & Communications Theory
- √ Radio Direction Finding
- √ The particular sequence of ten words "attack on an English writer that the character of this" is not at all unreasonable.
Science in the news: New elements
- √ Polya's Ten Commandments for Mathematics Teachers
- √ incenter
- √ incircle
- √ circumcenter
- √ circumcircle
- √ A circle is defined by three points
- √ darmstadtium
- √ roentgenium
- √ copernicium
- island of stability
Electrical Engineering & Communications Theory
- √ Perspector
- √ Encyclopedia of Triangle Centers
- √ Semiperimeter
- √ Menelaus
- √ Giovanni Ceva
- √ Stewart's Theorem
- √ The Three Kinds of Circles Associated with a Triangle
- √ Angle Bisector Theorem
- √ altitude
- √ Equation of a Line Normal to a Second Line, and Containing a Point on the Second Line
- √ Excenter
- Ceva's Theorem (yeah, I think I need to rewrite that. It's pretty key to the geometrical concept of the point of concurrency, which also needs to be written. *SIGH*)
- Cevian triangle
- Contact triangle
- Excenter contact triangle
- Extangent triangle
- Median triangle
- Orthic triangle
- pedal triangle
- anticomplementary triangle
- Geometric Notation
- Gergonne point
- Nagel point
- symmedian point
- de Longchamps 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
- Radical axis
- "Paradox", a poem by the mathematician Clarence Wylie
- Bevan point
- Schiffler point
- Brocard points
- Brocard angle
- Conway notation
- isotomic conjugate
- isogonal conjugate
- Clawson point
- Triangle center function
- Power of a point
- Miquel's Theorem
- 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
- C.a.R. - Interactive Geometry Software
- Cut the Knot
- 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
General Math Topics
- Madame Bovary
- (Great Books reading list)
Chinese Space Program
Slice of Life
- Frank Ramsey
- Ramsey Theory
- geometric mean
Jet-Poop's decaversary interview answers.... that's going to take a while to write. A novella begging to be written.
- √ November 6, 2011 daylog & Iron Noder progress
- √ November 15, 2011 daylog & Iron Noder progress
- √ November 24, 2011 daylog. Rediscovering the poet Edna St. Vincent Millay, which prompted thoughts which led to this
- √ November 25, 2011 frustration with server crashes
- √ November 30, 2011 daylog, mostly on my geometry nodes, which are being developed at an excruciatingly slow pace. This is turning into a damned textbook.
- √ Books you haven't read in a while, but intend to read again
- √ jessicapierce as a unit of quality A pesky idea that wouldn't go away until I wrote it down.
- (Great Books reading list)
- (Distance Running Progress)
- On being newly thin
A node you should read: The Awful German Language Part 2, by id1984, a writer new to me. This node has been around for eleven years, but I'd never run across it until just the other day. Typical for E2 - hidden gems everywhere.