Updated with new discoveries 31 January —11 February 2015; first published 27 May 2014. (Incidentally, new type of pentagonal tile discovered July 2015 by Casey Mann, Jennifer McLoud-Mann, and David Von Derauc.) For these examples and a proof that symmetry groups with order three rotations cannot occur, see John Berry, Matthew Dannenberg, Jason Liang, Yingyi Zeng, Symmetries of Cairo-Prismatic tilings, Rose-Hulman Und. Math. J. 17 (2016), http://scholar.rose-hulman.edu/rhumj/vol17/iss2/3.
A joint paper [C1] with my SMALL undergraduate research Geometry Group found least-perimeter pentagonal unit-area tiles, Cairo and Prismatic:
They proved that mixtures of unit-area convex pentagonal tiles can do no better, but found many examples of Cairo-Prismatic tilings that do equally well [C1, C2]. Since their work nine more have been discovered. Continue reading ‘New Optimal Pentagonal Tilings’ »
I’ve spent Fall 2014 of my sabbatical year from Williams College at Berkshire Community College as Visiting Professor (teaching developmental algebra) and Special Assistant to the President. I went because I had gradually come to feel that community colleges are where education meets the future, with the full diversity of students of all ages, backgrounds, interests, histories, part time and full time, soon to comprise a majority of all American college students. I went because I loved the president (Ellen Kennedy) for her understanding of the place, her vision for the future, her humble openness in dealing with everyone. I taught beginning developmental algebra (MAT 028) because it is the most problematic course, the major barrier to students’ making it to graduation, a course in which a third of the students withdraw, a third fail, and only a third pass.
Despite the lack of funds and the challenges faced by students, faculty, and staff, everyone loves the place and its possibilities. It was an honor and a joy to be part of it. See guest blog posts by my generous colleagues Donna Kalinowsky, math chair Nancy Zuber, and Fayette Reynolds.
I had two Williams colleagues and friends down to visit. Ed Burger, now President of Southwestern University, spoke on “The Five Elements of Effective Thinking.” Colin Adams did his “Zombies and Calculus“; see his Nova Video 1 and Video 2. I established a high school speakers bureau. I ran a Friends of Math luncheon series. I organized a bus trip of over forty students, faculty, and staff to visit the Museum of Mathematics in New York City. I wrote a Huffington Post blog on “Adding Fractions.”
I was interviewed on Rick Chrisman’s “1350 West Street” local TV show, Part 1 and Part 2.
OTHER RELATED VIDEOS: Continue reading ‘Berkshire Community College’ »
The following post was written by one of my star algebra students at Berkshire Community College, in a desire to help students in similar situations.
“Ready or Not” by Aaron Biros
The harshest thing each of us faces on a daily basis is a wakeup call. This could mean the wretched sound of that insufferable alarm clock, a pathetic paycheck for an epic work week, or struggling through a class you hate. Regardless of which of these haunts your thoughts, they are part of the many challenges of success. From my experiences thus far, the best opportunity any of us have to advance ourselves socially, intellectually, and, of course, financially is through education and perseverance. Realizing this for myself was a harsh wakeup call for sure. Continue reading ‘Algebra Student Exhorts his Peers to Make the Most of their Opportunities’ »
Guest post by Fayette Reynolds, Professor of Life Sciences, BCC
We have many sturdy, fortunate and accomplished students who come to Berkshire Community College (BCC) for practical reasons. But there are also many students who have difficult histories, who carry overwhelming personal burdens. They may not know or believe in themselves. Nor do they believe in the possibility of a fresh start, or new direction. BCC is a place where we look at our students with fresh, curious and affectionate eyes. We believe in them and in their courage, their strength and their potential to create productive and significant lives. They are remarkable.
Whenever I myself felt overwhelmed I would call my dad, and he would laugh and say to me, “Be like a leaf floating down a stream. Just keep your head above water.” Just don’t give up.
Guest post by Nancy Zuber, Professor of Mathematics and Chair, Berkshire Community College
One of the best days of my life was when my engineering students graduated from Berkshire Community College. I had tortured them through five courses over two years with relentless problem sets and exacting two-hour exams. As the students paraded by us faculty after the ceremony, one of my students came right up to me, hugged me, and said, “Thank you.” Then another student came right up to me, hugged me, and said, “Thank you.” Over and over it kept happening, the same thing, the same “Thank you.” After the ninth and last one, I was euphoric; I found myself approaching my husband in tears. The joy lasted for days. And they still come back and see me.
Derek Carroll describes his path toward a PhD in astrophysics.
On crutches after a recent bicycle mishap, I’m getting a sense of what it’s like to be handicapped at college. Everything takes longer, it’s hard to get from one event to another on time, and you have to depend on other people. That last inconvenience, dependence on others, can be a blessing. Here at Berkshire Community College (where I’m spending part of my sabbatical) I’m finding the kindness of others a source of much comfort and joy. When I arrived the first day on crutches, a student, already late for an appointment, took the time to help me up the banks of stairs from the parking lot and carried all my stuff for me. Security promptly provided me with more convenient handicap parking. My third example is one that few schools could match: as I stood in line at breakfast, wondering how I would get my tray to a table, President Ellen Kennedy appeared on her way to an appointment and carried my tray to my table for me. Continue reading ‘Handicapped at College’ »
Had a great time Saturday (26 July 2014) with my 2014 Geometry Group at the Summer Program for Mathematical Problem Solving at Siena College, a three-week program for 38 mathematical talented middle schools students who go to low income NYC public schools. We presented Soap Bubbles and Mathematics, including a little guessing contest with demonstrations, explanations, and prizes, won by Rashik Ahmed. Photos show in action my students Bryan Christopher Brown, Alyssa Loving, Wyatt Boyer, and Sarah Elizabeth Tammen.
I am excited about spending part of my sabbatical this fall at Berkshire Community College. I’d say that community colleges are where education meets the future. It looks like next year for the first time a majority of US college students will be at community colleges. So far everyone I’ve met loves the college and its President. Here’s an account, “The Good Things,” by one of the math adjuncts and one of my best new friends, Donna Kalinowsky, of some of the reasons she loves the place:
Continue reading ‘Donna Kalinowsky on Berkshire Community College’ »
Friends, mathematicians, scientists, and the public celebrated the 70th birthday of distinguished mathematican Jean Taylor at the Museum of Mathematics in New York City, Saturday evening, September 6, 8-10:30 pm. It was Taylor who proved Plateau’s rules for soap bubbles. I wouldn’t miss it. You can register for $25 (additional donations completely optional and not specifically for Taylor celebration). There was also a little symposium of 5- to 15-minute talks 1 pm Saturday afternoon at the Courant Institute at NYU (photos thanks to Christina Sormani). See comments for well wishes.
Continue reading ‘Jean Taylor’s 70th at MoMath’ »
Just as a a soap bubble minimizes surface area, crystals minimize a more general energy depending on orientation with respect to the underlying crystal lattice, given by integrating some (continuous) norm on the unit normal. (One might drop the usual assumption that a norm is even.) The optimal shape is the unit ball of the dual norm, called the Wulff crystal (see [M2, Chapt. 16]). Continue reading ‘Clusters for General Norms’ »