Quick: What's wrong with this photo?
It's winter time. Let's talk about snowflakes.
Doing it all wrong
Did you ever make paper snowflakes in elementary school?
If so, you probably made them like the picture above. (Or maybe the picture below, if you had a really adventurous teacher.)
You were also probably told that no two snowflakes are alike, and you imagined a myriad array of possibilities. You were also, surely, led to believe that snowflakes are symmetric (with symmetries governed by the dihedral group Dn for some n).
But all of that is bogus, and has been known to be so since 1611!(*) Perhaps the most annoying thing is that the truth is more exciting than this fiction... Kepler's paper, "A New Year's Gift, or, On the Six-Cornered Snowflake," is widely considered the origin of the sphere-packing problem that has piqued mathematicians' and grocers' interests alike for hundreds of years. Anyhow, the facts are:
- the only possible symmetries are n = 3, 6, 9, 12, ..., with n = 6 accounting for the lion's share;
- the likelihood that a naturally occurring snowflake is actually (6-fold) symmetric is ZERO;
- snowflakes are far from unique, indeed every snowflake begins as a hexagonal disc, and remains so for quite awhile;
- the imagined myriad array is, in fact, only a 5 x 7 table of possibilities.
The truth is more physics than mathematics, but, as a "symmetry" in nature, it is one of the many things you might learn about in Giaquinto's HONR 204 course. You might also try the 2001 book by the estimable British mathematician Ian Stewart.
How to do it right
It's not too hard to fold paper in a way that will give you 6-fold symmetry. Here's one tutorial.
(Final quiz: what happens if you skip the last fold depicted at bottom-left above?)
And here's Vi Heart to take us out.
More Featured Stories
Ignatian HeritageFor Loyola junior Lizzie Sextro, this year’s Ignatian Heritage Month will feel a lot different than last year’s. That’s because Sextro spent 10 days in July in El Salvador, where she got a first-hand look at the site of the Salvadoran martyrs’ deaths.
Ignatian HeritageIgnatian Heritage Month kicks off with Loyola’s annual Hunger Week, a series of events from November 3–9 to raise awareness about hunger issues locally, nationally, and globally.
Ignatian HeritageLoyola is honored to host Jon Sobrino, S.J., for an address commemorating the 25th anniversary of the Salvadoran martyrs. Father Sobrino will speak on November 20 at 6 p.m. in Mundelein Auditorium. Registration is required.
November 7The annual International Symposium on Digital Ethics brings together scholars and thinkers to discuss a variety of topics. This year's symposium will feature a keynote address by Anita Sarkeesian, media critic and creator of “Feminist Frequency.”
In the news10-29-14-SSW-wheeler-scroll
QuinlanHuy Nguyen (MBA/MSF ’14) lost his job in the 2008 financial crisis. Then, he watched as other members of his family lost theirs, too. So he came to Quinlan for graduate school—and to learn how to prevent future financial meltdowns.
ResearchLoyola psychology professor Grayson Holmbeck has been studying children with spina bifida for more than 20 years. In that time, he says: “We’ve learned a lot about what their problems and issues are, what we can do to help them, and more importantly, what they’re capable of.”
Adult LearnersStarting in 2015, Loyola will offer several FASTRACK degree programs for adult learners at its Cuneo Mansion & Gardens in Vernon Hills. Courses will be on alternating Saturdays with an online component—perfect for anyone looking to balance work, life, and school.
Professor profileQuinlan Professor Nenad Jukić was named Loyola’s Faculty Member of the Year on September 14 as part of the University’s Faculty Convocation. This latest award caps off a string of impressive accolades for Jukić, who also was named Quinlan’s Outstanding Undergraduate Teacher of the Year.
Helping othersFour Loyola graduate students were recently selected for the prestigious Albert Schweitzer Fellowship program and will spend the next year working on healthcare-related projects to help underserved communities in Chicago.
AcademicsLoyola is one of just 283 universities to have a Phi Beta Kappa chapter, a claim that only about 10 percent of the nation’s colleges can make.
SustainabilityLoyola is ranked No. 4 on the Sierra Club’s 2014 list of the greenest colleges in America. The annual rankings are designed to spotlight universities that are deeply committed to environmental responsibility.
In the newsLoyola’s Information Commons joins an elite group of peers on Business Insider’s list of the “coolest” college libraries in the country.
ExploreThe Institute of Environmental Sustainability combines academics and research with agriculture and community living—all in one facility.
Damen CenterThe Damen Center was designed from top to bottom with students in mind, making it the center of social life on Loyola’s Lake Shore Campus.