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Frank Morgan

Frank Morgan's work in minimal surfaces spans over 150 publications and six books, including the popular Math Chat Book, based on his live, call-in Math Chat TV show and Math Chat column. He was undergraduate mathematics chair at MIT, then mathematics chair at Williams College, founding director of the "SMALL" NSF undergraduate research project, vice-president of the Mathematical Association of America, vice-president of the American Mathematical Society, and is currently Webster Atwell ’21 Professor of Mathematics at Williams College. Work partially supported by National Science Foundations grants.

Entries by Frank Morgan

Adding Fractions

(0) Comments | Posted March 14, 2014 | 5:28 PM

Mathematics has got to be the most interesting of all subjects. As I was telling the wonderful math faculty at Berkshire Community College, even arithmetic is fascinating. Addition and multiplication are commutative: 4+7=7+4 and 4x7=7x4. I recall MIT Professor Michael Artin saying:

When I ask my kids what's 4x7, they...
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Are Smaller College Calculus Classes Really Better?

(4) Comments | Posted August 26, 2013 | 10:41 AM

An unpublished study* from the late 1990s showed that calculus students in classes of about 35 do no better than students in classes of 90 and larger. There was no statistical difference in the amount learned or in the drop-out rate. The large and small sections were taught...

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Dark Matter and Worst Packings

(2) Comments | Posted May 28, 2013 | 1:35 PM

The annual Geometry and Topology Conference at Lehigh University attracted over 60 mathematicians from around the world. Hugh Bray of Duke University talked about a possible explanation for the mysterious dark matter, known only by its gravitational effect, more than five times as abundant as regular...

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How Often Should I Rebalance My Investments?

(0) Comments | Posted December 3, 2012 | 7:20 AM

Investment experts will tell you that the keys to successful investing are diversification and rebalancing. This means that (1) you should buy a diverse collection of stocks and bonds and (2) you should maintain the percentage of your money of each. Diversification guards against large fluctuations in certain industries or...

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Why I Don't Like Energy-Efficient Light Bulbs

(32) Comments | Posted November 24, 2012 | 1:14 PM

The theory is that traditional (incandescent) light bulbs waste lots of energy by producing more heat than light. Let's look at the bigger picture. I'm a big fan of saving energy: I go shopping with my car just once a month, I keep the thermostat at 50 degrees, I turn...

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The Fastest Path Around the Bases

(13) Comments | Posted October 19, 2012 | 1:20 PM

When Prince Fielder hits that final long ball in the World Series and knows he needs the home run, what is his fastest path around the bases? If he runs straight for first, he either has to slow to a near stop or go sailing far beyond into the outfield....

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U.S. Presidential Election Paradox

(0) Comments | Posted October 16, 2012 | 8:12 PM

Question: What is the fewest number of votes with which you could be elected President of the United States? Say that there are just two candidates and that half the population in each state votes. Hint: You can win with fewer than half the votes.

Answer. Technically you just need...

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MathFest: Teach Meaning or Procedure in High School Mathematics?

(0) Comments | Posted August 6, 2012 | 11:54 AM

Last weekend a near-record 1500 mathematicians gathered in Madison, Wisconsin, for the summer meeting (MathFest) of the Mathematical Association of America (MAA). That 1500 included over 200 undergraduates; the majority gave talks on their own research. My three students presented their new discoveries about...

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Why a Laptop Is Not a Computer

(14) Comments | Posted July 24, 2012 | 3:03 PM

The personal computer unfortunately has lost one of the most basic and useful features of the earliest computers. Let's say you're surfing the web. You find something and want to copy both the web address and a few lines for a friend, but you can copy only one thing at...

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Spilled Orange Juice on My Way to a Math Conference in Spain

(0) Comments | Posted June 30, 2012 | 12:58 PM

I was already worried when he asked for his dinner in one hand while he still had his computer open on his dinner table. It was a full flight and he was a big guy. I had my newly arrived dinner, with my water and orange juice, in front of...

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I Win Soap-Bubble-Cluster Controversy

(6) Comments | Posted June 22, 2012 | 2:43 PM

Planar (flat) soap bubble clusters seek to enclose, say, N unit areas with the least amount of fencing:


The best single bubble (N=1) is a circle, the best double bubble (N=2) is two overlapping circles with a straight line down the middle,...

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Why Is Summer So Early (June 20)?

(27) Comments | Posted June 17, 2012 | 8:06 PM

A century ago, in 1912, summer arrived here in Massachusetts at 1:17 p.m. on June 21. This week it arrives almost a day earlier, at 5:09 p.m. on June 20. Both years are leap years (which by inserting an extra day makes summer arrive earlier), so that doesn't explain the...

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Math Now -- Commencement Can Wait

(0) Comments | Posted May 28, 2012 | 5:42 PM

I've been spending the week before commencement, while my college officials decide which students get degrees and prizes, enjoying a week of mathematics events up and down the east coast.

Wednesday morning I visited the spectacular new home of the new National Science Foundation mathematics institute at Brown University,...

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Geometry Festival

(3) Comments | Posted April 30, 2012 | 8:56 PM

Some hundred mathematicians gathered at Duke University this past weekend for our annual "Festival" of the latest new results in geometry. Fernando Coda Marques of IMPA in Río de Janeiro, Brazil, reported on his new proof with André Neves of the Willmore...

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Math Finds the Best Doughnut

(19) Comments | Posted April 2, 2012 | 8:30 PM

After a 47-year search, mathematicians Fernando C. Marques and André Neves have found the best doughnut, or at least the best geometric shape for a doughnut, pictured in Figure 1, with the narrow hole only about 17 percent (3-2√2) of the width of the doughnut. "Best" for mathematicians means the...

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Soap Bubbles in Scotland

(6) Comments | Posted March 23, 2012 | 3:21 PM

Lord Kelvin's 100-year-old problem has been under attack this past week at the International Centre for Mathematical Sciences in Edinburgh, Scotland. In his attempts to understand space as an etherial foam of unit-volume bubbles, Kelvin sought the most stable, least-area such structure. Kelvin conjectured a structure...

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Alan Alda's Flame Challenge and Kids' Five Most Popular Science Questions

(0) Comments | Posted March 16, 2012 | 11:07 PM

The actor Alan Alda challenges you to explain to an 11-year-old what a flame is.

The winning entry will be announced at the World Science Festival in New York in June. According to researchers for the Big Bang United Kingdom Young Scientists...

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Can Math Survive Without the Bees?

(47) Comments | Posted March 6, 2012 | 10:04 AM

The recent reports on the disappearance of bee populations have omitted mention of their role in the longest-standing open problem in mathematics, dating from the first millennium B.C.E. and solved in the nick of time (actually with a year to spare; see Scientific American) for the second millennium...

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