Math, Teaching, and Other Items of Interest
In a regional online ACBL bridge tournament today, I was sorry to hear my LHO open 1D, my partner Bob Cole overcall 2C, my LHO double, and my RHO pass. Sounded bad, so I tried 2H, P, P, x. Still sounded bad, so I tried 2S, x, P, P, P. This one made for a top.
At the LVBA virtual open bridge game with Mike Kohler today, I found myself as North in an unhopeful 3N after East showed Hearts and Spades. After two Heart tricks, two Diamonds, and a Heart, I seemed a trick short. But as I ran the Diamonds West erroneously discarded a Spade. At this point I held A9 of Spades with QJ on the board. I cashed my only Spade stopper, finessed the Club Ten to West’s Q, and held my breath. If East did not have the remaining Spades as her bid promised, West could get out with a Spade to set me a couple of tricks. But here as I hoped West had to return a Club, making my Club J the ninth trick. Jim Berry has pointed out a similar endplay of East by first cashing the Club Ace, which does not depend on any defensive error.
In January 2020 I taught a Williams College Winter Study course on “Tournament Bridge,” including five days at a regional tournament in Tarrytown NY. All participants came home winner with Master Points. In the pictured board Saturday morning January 25, Jihoon Kim and I held the NS cards. Jihoon passed and West opened 1C. Since the opponents apparently held all the cards, I tried a daring weak jump overcall of 2H. The opponents still reached the optimal contract of 3N, but Jihoon now knew to lead a H, first the K and then the 2 to Declarer’s Ace. (Actually Declarer should have taken the A on the first trick, leaving a stopper in dummy.) My Hs are now good, but with only the slim prospect of getting in with the DQ, and E can easily and safely finesse into South’s hand. But
2 and 6 of Ds, unguarding my Q. The observant Declarer was then so sure that South had the DQ that he immediately took the losing finesse into my hand, allowing us to cash three more Hs and the CA for down 2 for 93 percent.Much enjoyed Israel in April 2019 with the perfect host, Emanuel Milman, who invited me to give a series of lectures in Haifa at Technion and showed me good restaurants, Akko, and the beach. I spent my third week in Jerusalem at the Imperial Hotel in the Old City, right inside Jaffa Gate. My first explorations took me down narrow cobblestone streets to what Constantine’s mother Helena identified as the spot where Jesus was crucified and buried; she had the Church of the Holy Sepulchre build around it. 
I similarly loved the alternative Garden Tomb site, attended a Good Friday service there, and entered the tomb (Photo 1). I also loved the Wailing Wall (Photo 2), resolved to overcome suffering, and inserted a slip of paper in a crack. 
On the other side is the Temple Mount, site of the Solomon’s Temple (destroyed by the Babylonians), Nehmiah’s rebuilding (destroyed by the Romans), 
and currently two Muslim mosques (Photo 3). The Garden of Gethsemane is nearby (Photo 4). 
Not far outside the current walls is the City of David, where I ventured through Hezekiah’s long, low, narrow, pitch-dark water tunnel, with the water up to 2-1/2 feet deep, to the Pool of Siloam. I also enjoyed playing bridge in Haifa (at the Carmel Club) and in Jerusalem (at the Bridge Center and once at Wizo). Afterwards I spent a week in Cairo at the Grand Royal Hotel near the Nile (Photo5), on “My Undercover Mission to Find Cairo Tilings.”
Stanley Sterenberg has kindly provided this encouraging story about the sometimes unrecognized potential of a student. He writes, “Alexa is interested in inspiring students, especially young girls pursuing STEM careers, and is eager that what she and I refer to as ‘our story’ be posted.”
I was a math teacher for 21 years, at various points teaching grades 4 through 12. One year, while teaching an advanced seventh-grade class, I taught a student named Alexa. Alexa was, in my opinion, a solid student, but by no means an outstanding one.
Two years later, I observed a ninth-grade geometry class where Alexa was making a presentation on a topic she had researched. Despite my Ivy League college math degree, I could barely follow the details of her talk, and I left thinking two things: Alexa was a brilliant math student, AND, how could I NOT have seen this two years earlier? Continue reading ‘A Student’s Unrecognized Potential’ »
I traveled to Shanghai in February 2019 to teach a 10-day research seminar for the Institute for Advanced Research for what turned out to be just five high school students. At breakneck pace, I provided an introduction to Riemannian Geometry, including Gauss, sectional, Ricci, and scalar curvature, General Relativity, the Gauss-Bonnet Theorem, geodesics, and general norms. In addition, the students undertook an original research project, resulting in a published paper on “Isoperimetric Problems on the Line with Density |x|^p” Continue reading ‘China’ »
Frank Morgan’s 2019 Geometry Group in SUMRY at Yale: Jack Hirsch, Kevin Li , Jackson Petty, Christopher Xue.
Research Problems
1. Perelman’s stunning proof of the million-dollar Poincaré Conjecture needed to consider not just manifolds but “manifolds with density” (like the density in physics you integrate to compute mass). Yet much of the basic geometry of such spaces remains unexplored. Recent results after Chambers ([8], [10]) show in various cases that if balls about the origin minimize perimeter for given volume if they are stable. Major open cases include hyperbolic space with radial density [9]. For a log-concave radial density such as e-1/r, isoperimetric curves probably pass through the origin, like the isoperimetric circles for density rp [4]. Double bubble in plane with density rp would be interesting. See references [1-11] below.
Nat Sothanaphan wrote this article as a high school student in 2011.
Today in Easton sitting East I bid Michaels 2S after 1S-P-1N, showing hearts and diamonds, and my mom passed! We made 2S for a near top.
Nat Sothanaphan wrote this article in Grade 12.
Welcome to my blog. I also have a blog at the