Carnival of Mathematics 180
/In which this blog hosts the traveling carnival, founded by the fine folks at aperiodical.com
This is number 180 in the series, which I suppose means this has been going on for some 15 years. Tradition has it that I should give some interesting facts about this number. The prime factorization is \(2^2\cdot 3^2\cdot 5\) and so our hero has the largest number of factors of any number so far (Wikipedia tells me such numbers are called highly composite). It fits neatly between the twin primes 179 and 181. It is the number of degrees in half a circle, the sum of the angles of a triangle (in the Euclidean plane, of course), the sum of two squares (144 and 36), the sum of six consecutive primes (19+23+29+31+37+41), and it is a 61-gonal number.
As I write this, the world is consumed by the COVID-19 pandemic. My university, like most others in the United States, has moved its classes online for the remainder of the spring term. My local government (Alachua County, Florida) has issued a shelter-in-place order, designed to minimize social contact. I am working from home, as is my wife, and our son is home from his North Carolina university, completing his courses online. I have purchased plenty of dry goods (rice and beans, mostly), and we’re all trying to make the best of it. I hope that wherever you are reading this that you and yours are safe and healthy.
If you’re anything like me, you’ve been reading lots of articles about modeling the spread of the coronavirus. Some of these are rather grim, but very informative. This one, by Tomas Pueyo, made the rounds on Twitter; it’s worth a read. One of my colleagues, a mathematical biologist, shared this one by Alvin Powell, about the idea of on-again/off-again social distancing as a strategy. Jay Daigle wrote a nice explainer of the SIR model for epidemics.
But enough of that. I assume you read the news and have seen the predictions. How about some non-pandemic math? I received several submissions:
We all know the apocryphal story of a young Gauss correctly finding the sum of the first 100 positive integers in a few seconds. Tom Edgar and Enrique Trevino shared a collection of proofs of the formula for the sum of the first \(n\).
Benjamin Leis shares a good activity relating Pascal’s triangle to Vandermonde’s Identity.
From Games4Life, a connection between tessellations and the Fibonacci sequence.
The Klein bottle, via JA Sites.
Dynamical systems are fun. Here’s an introduction to stability by Ari Rubinsztejn.
And, I want to plug this one, by my podcast co-conspirator Evelyn Lamb (which brings to mind this great song).
Quanta Magazine had some nice articles this past month. Anyone who has ever visited the Mathematisches Forschunginstitut Oberwolfach knows what a special place it is; this article by Kevin Hartnett sums it up nicely. Susan D’Agostino had a nice interview with Ronald Rivest. Erica Klarreich speculated about the geometry of the universe.
If you’re into audio and video, may we suggest the following?
(ahem) My Favorite Theorem featured Ben Orlin in March (sorry for the shameless self-promotion).
Grant Sanderson (3blue1brown) released an excellent video about COVID-19.
Rob Ghrist released the first part of his video series on Applied Dynamical Systems.
That’s it for this edition of the Carnival. Carnival 181 will be hosted by Ben at Math Off the Grid; submission instructions available at the link to The Aperiodical above. In the meantime, stay home, wash your hands, and keep you and yours safe. Be well, everyone.