Adoption and Reform of the Gregorian Calendar

Everyone knows that George Washington was born on February 22. Every mathematician knows that the year was 1732 (because 1.732 is the beginning of the square root of 3). As are so many facts known to everyone, neither of these is wholly correct. In 1752 we changed the way we keep track of dates because our calendar had drifted from its astronomical benchmarks. The problem is the earth does not go around the sun in a considerate number of days, but rather approximately 365.2422. In addition the moon goes around the earth in an inconsiderate 29.53059 days (approximately). This is 29 days and about 12 hours, 44 minutes, and 3 seconds. In other words a calendar based on celestial phenomena is necessarily imperfect.

Quadrilaterally Speaking

Among the figures of plane geometry, the triangle holds a special place. Triangles are simple, basic, and unembellished, yet their geometric importance cannot be overemphasized. All have three medians, three altitudes, and one centroid, and all possess both inscribed and circumscribed circles. When two or more triangles get together, they can be the spitting image of one another (i.e., be congruent) or at least bear a strong family resemblance (i.e., be similar). And as everyone knows, congruent and similar triangles are critical to the logical development of geometry.

A Better Way to Memorize Pi

How I wish I could elicidate to others: there are often superior mnemonics! In the April 1999 issue of Math Horizons, Mimi Cukier discusses classic and original sentences and poems, whose word lengths provide the first few digits of pi. The first sentence of this paragraph is another such example.

Geniuses and Prodigies

One of the most romantic episodes in the history of mathematics occurred one morning in January 1913, when professor G. H. Hardy received a strange-looking letter from India. At thirty-six, Hardy was a renowned mathematician, probably England's most brilliant. Professor at Trinity College in Cambridge, he had recently been elected a fellow of the Royal Society. There he often conversed on equal terms with minds as remarkable as Whitehead and Russell. So one can imagine his growing irritation as he skimmed through this letter posted in Madras. In rudimentary syntax, an unknown Indian named Srinavasa Ramanujan Iyengar requested his opinion on several theorems.

Stopwatch Date

Sophie Claire Meuth of Normal, Illinois was born on the last day of November 1999. What her parents, Jeremy and Alison, didn't realize as the time was that their daughter was born on a special date--the date that was overlooked throughout all the millennium hubbub--November 30, 1999: The Stopwatch Date.

A Very Simple, Very Paradoxical, Old Space-Filling Curve

In July 1938, Douglas "Wrong-Way" Corrigan flew nonstop from California to New York in 28 hours (a record!?!). On his return flight to California he apparently became disoriented in the impenetrable fog and ended up, 24 hours later, landing in Ireland! (His plane had a faulty compass and no radio.) He was given a hero's welcome when he returned to the States. Mathematicians have long known a space-filling curve which has certain similarities to Corrigan's flight.

Sleuthing Around the CDC

It is hard for me to believe that I did not know what a biostatistician was just ten years ago. I guess it is not surprising then that not everyone understands when I tell them I am a biostatistician. Explaining that biostatistics involves the use of statistics in the area of public health doesn't always convey what this actually entails. When I say I work for the Centers for Disease Control and Prevention (CDC) in Atlanta, Georgia, most people get a glimmer of recognition. I think most people appreciate the work that goes on at the CDC. I was interested in how they conducted research at the CDC long before I had heard of biostatistics or realized how statistical methods were used in the detective work being carried out at the CDC.

A Dozen Questions about Squares and Cubes

Have you ever reflected upon all the remarkable things you can do with a simple square? Stacking together four copies of this shape, for example, produces a larger copy of itself. Repeating this self-replication ad infinitum yields a square tiling of the entire plane, leading one to a whole host of intriguing results in walking and tiling. Many of these properties generalize to the third dimension inspiring problems involving cubes and cubical lattices in three-space. As we have seen, gluing together the edges of squares produces donuts, Klein bottles and the like, and gluing together faces of cubes leads to higher dimensional "surfaces."

The Final Exam: The Augsburg Puzzler

(To read the winning entry to September's Final Exam, click here.)

Augarithms is the biweekly newsletter of the Augsburg College Mathematics Department. Each week we run a brainteaser, "The puzzle of the week," whose solution generally requires cleverness, insight, or sideways thinking rather than prowess in technical mathematics. Collected below are a baker's dozen of puzzles featured recently in Augarithms. This month's Math Horizons contest is to solve these puzzles. Send your solutions in by April 1. Several randomly selected respondents from among the most successful solvers will receive Math Horizons t-shirts.