Archive for the ‘Articles’ Category.

Israel

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.”

 

 

A Student’s Unrecognized Potential

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.”

Why We Teachers Need to be More Humble

by Stanley Sterenberg

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’ »

Geometry Group 2019

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.

Continue reading ‘Geometry Group 2019’ »

On Construction Using Construction Tools of Finite Size

Nat Sothanaphan wrote this article as a high school student in 2011.

On Construction Using Construction Tools of Finite Size

Passing Michaels Yields Top

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.

The Urinal Problem

Nat Sothanaphan wrote this article in Grade 12.

Urinal Problem

Is Making 6N Better Than Making 7N?

Playing at the Bethlehem Bridge Club with Frank Kuebler November 20, 2017, I was North in 6N. It’s 100% on the diamond lead if you’re careful. You can’t go to the board with the Heart Ace to take the club finesse because if it loses you lose a club and a heart (although as the cards lie you’d make 7N here). You can’t even lay down the Club Ace , lest an opponent with four Clubs holds up and cuts your communications (although as the cards lie you’d make 7N here). The guaranteed line is to lose a club and keep the Ace to access the spades in hand.

6S at the Toronto Bridge Club

On July 17, 2017, at the Toronto Bridge Club, my partner Paul Selick and I got to 6S by me in the East. After South played HJ on the second Heart, which I ruffed in dummy, I played for a 3-3 Heart break (which would let me make 7) and went down 1.  Greg Lawler pointed me to the best line: draw trump, overtake the Diamond King with the Ace, and take the Heart finesse. It loses, but a ruffing finesse brings home the Hearts. Note that this line also works if North has both Heart honors, as long as Hearts are no worse than 4-2.

A Squeeze at the Penultimate Trump

On the pictured hand 13 at the Pembury Bridge Club in Pittsfield MA on Wednesday June 14, 2017, as East I made 3S, losing a trick in each suit. After ducking the heart lead and winning the continuation, I could have made 4 by reaching a position with DA5 and H7 in my hand, DJ8 and CJ on the board, and South down to HQ and DQT. Leading my heart endplays South in Diamonds. Peter Winkler explained to me how to make 4 on a Club lead (the previous endplay cannot afford a club loser). After losing e.g. a Club, a Heart, and a Spade, play Spades from dummy, coming down to S53, DJ84 in dummy. Now on the penultimate spade, come down to DAK, Hxx in hand, and South cannot protect both Diamonds and Hearts. (If North leads a Diamond when he gets in with a Club, East will be left with the HA as the second entry to hand. Play Spades in a way to prevent North from getting in to lead Diamonds twice. Curiously, when they start with Hearts, you need to play Spades the other way to prevent South from giving North a Heart ruff.)

Amazing AMS spring sectional in Pullman WA

I just attended an amazing constellation of events around the AMS spring sectional meeting Saturday/Sunday April 22-23, 2017, in Pullman, Washington, organized by Kevin Vixie of Washington State University.

The meeting was preceded by a day on Data Science, with an incredible variety of short talks every 15 minutes, interspersed with discussion periods. Continue reading ‘Amazing AMS spring sectional in Pullman WA’ »