## JoHN MiLLeR## Portland, Oregon
I first corresponded with Martin Gardner in 1968 about
Langford's Problem (below).
I attended G4G10 (my first ## What Shape is a Tree? (2012)This short talk is based on some of the 150Geom-e-Treeson a poster designed by yours truly.
Download PDF of More about the Geom-e-Trees Poster my talk is based on. ## Immersive iPad AppsI like to think Martin would've enjoyed these iPad apps I've published. Icons all by Gus Miller!
You can click on any of the icons to visit that app's commercial website. ## Langford's Problem (2014)In November 1967, Martin Gardner challenged readers to arrange 4 pairs of colored blocks in a certain way. He told readers that no solutions were possible with 5 or 6 pairs, but that there were 25 unique arrangements for 7 pairs (no references cited). Early in 1968, as a freshman at Gonzaga University, I programmed Langford's Problem and found 26 (not 25!) solutions for n=7 and 150 solutions for n=8. Three or four others did likewise. E.J.Groth cracked n=11 and n=12. Martin published these results in March, 1968, thus beginning decades of correspondence as solutions for higher values of n were computed by myself and others. Click on the colored blocks above to land on my highly-referenced page on Langford's Problem. (Sorry, no interactive gizmos, YET.) Here is a video of my 12 minute G4G11 talk on Langford's Problem: Download PDF of On Langford's Problem. This paper was contributed to the G4G11 Gift Exchange Book, March 2014. ## The Music of the Polygons (2014)I gave a seven minute demonstration and talk about PolygonJazz. This was noted in Magic, Puzzles Delight Math Fans at G4G as:John Miller showed us how sound can be used to understand caroming billiard balls within polygons. Here is a video of my G4G11 talk: (I gave two talks at G4G11.) ## How Mathematical Games Enriched my LifeIn 1961, my 7th grade math teacher, Ray LaLonde, shared Martin's June 1961 Brain Teasers column with the class. I was hooked. After years of checking out previous columns in the library, I finally subscribed to Scientific American beginning in May 1964. when I was 14 years old! While on Sabbatical 1988-89, I went back through all previous MG columns and indexed them.Over the years, Martin wrote about: - philosophy, logic, paradox
- forms of infinity
- fairness in games
- history of mathematics and thought
- graph theory, finite state machines
- geometry, parity, topology, puzzles, fractals, origami
- magic tricks (eg. Kruskal's principle)
- the not-so-long arm of co-incidence
- and so on.
Martin would often combine several of these into a month's column, e.g. The Cycloid: Helen of Geometry.
I was interested in the popular culture of the early 60's, and had a very impressionable mind, so my first Dr Matrix column was practically traumatic. I thought Martin was sometimes A side benefit of that SciAm subscription was being exposed to the Amateur Scientist column, conducted by C.L.Strong. I was so interested in harmonography, I built the Double-Elliptical Pendulum Harmonograph. TO be fair, other writers continued the column (under various names). In my mind, I associate some of what they covered with Martin. But it was Hofstadter that covered Rubik's Cube (Mar 81), and AK Dewdney who covered the Mandelbrot Set and attractors (Aug 85), both of which were featured on the magazine cover. ## Math & Art- Squaring the Square, was written in 2014 as a COLUMN on a prototype Celebration of Mind website.
- The Immersive Bridge Between Math and Art, presented at Bridges in Baltimore, July 2012.
- D-ART Digital Art Gallery, 2012 Edition. (Not pleased with their website.)
- Stained Glass Exhibit
## A Mathematical Games IndexIn the 70's I started an index of MG on computer punch cards. While on Sabbatical in 1988, I completed a Subject Lines index of all the years of Mathematical Games and subsequent incarnations, such as Metamagical Themas, I made an attempt to categorize. I got Martin's permission to place my index on line. On October 23, 2014, I transferred the index to the MARTIN-GARDNER.org web site, so that it will have a more permanent home:
Also, some Wikipedians pirated my data and put up a wikipedia page covering the MG columns. They later figured out how to scrape the data from the publisher's website, and so they no longer reference my earlier work. But they don't have categories. They do reference other wikipedia pages that cover the concepts and problems, and that is good. Back to John Miller's Home Page |