107th Carnival of Mathematics
The number 107 is a Chen prime. Say what?
A Chen prime. Named after Mathematician Chen Jingrun, it is defined as any prime number p which exists such that p+2 is either a prime or a product of two primes. Obviously,107+2=109 is a prime number, thereby satisfying one of the above-mentioned conditions.
Also, the number 107 is the exponent of a Mersenne prime given by the form
which happens to yield thegargantuan value of 162259276829213363391578010288127. Don't forget 23 + 23 + 33 + 43 = 107. Rather neat don't you think?
Straying off for a bit, here are some other fun facts (not exactly related to maths though):
- 107 is the atomic number of Bohrium.
- There is a 107% rule which is applicable to Formula 1 racing qualifying sessions; this rule states that during the first qualifying phase, any driver failing to establish a lap timing within 107 percent of the fastest time in that phase itself will be disallowed from starting the race.
- A common designation for the fair use exception in US copyright law (read: 17 U.S.C. 107)
And so the carnival shall commence. Welcome to the 107th edition.
Football and Maths would seem to make an odd combination, but Oluwasanya Awe's post titled "An Optimization Problem: UEFA Champions League Standings" will set you thinking otherwise. He explains:
"I was inspired to look into the Mathematics of UEFA Champions League tables after the end of the group stages of the competition and I was fascinated by my observations."
Still on the topic of football, Matifutbol composes a piece which involves "a new signing, a public secret, sports betting, spirals, sunflowers, the Parthenon, and a Greek newspaper."
Some technicalities as well as Mathematical definitions were explained and explored in greater depth; Richard Elwes suggests serious readers spend time going through Skulls In The Stars's post about Abel summation and analytic continuation. He himself has also written at length about the "philosophy" of infinite series,as seen from this post of his. Colin Beveridge gives his two cents as well in the "Why The Maths of Infinite Sums Is Dangerous" post.
Alison Atkins feels terribly upset about Coca-Cola's recent Coke Zero advertisement in the UK, so much so she has taken to writing about all that's wrong with the ad itself.
Shecky R highlights an interesting error within an old problem/calculation from a classic Math volume by Edward Kasner and James Newman in her post titled "Polygons, Circles and Limits, Oh My… an interesting errata", while Jim Frost over at the Minitab Blog explains his preference for the standard error S over the coefficient of determination R2 in regression analysis.
It is common knowledge that 0! and a0 are both equivalent to the magical value of 1. But do you know exactly why? Peter Rowlett does a rather marvellous job in explaining this to students.
David Orden who writes at Mapping Ignorance poses an interesting question:
"Imagine you are a watchman, having to patrol some streets. Today you are assigned to straight, well-illuminated, and wide streets, that can be checked with a glance from the intersection. Before starting the route, you want to determine the shortest route allowing to check all your streets. How difficult can this be?"
Apparently not quite a walk in the park, as he attempts to break down the complexity of this problem in a recent post of his.
And then we move on to the topic of names. There is xkcd's oddball yet humorous discourse about baby names and their statistical occurences, and there is also a treatment on the appropriate collective noun-naming for Mathematicians of various fields over at Scientific American.
Before I conclude this edition, do check out John Cook's thoughts on rational cosines, and my derivation of the Lactus Rectum of a Hyperbola.
Hope you will have as much fun lapping up the offerings here as I did in presenting them. Peace.
6 February 2014
Do note that the next edition of the Carnival of Mathematics will be hosted at Math Hombre.
(PS: I would like to accord a sincere thank-you to Katie Steckles for giving me the opportunity to contribute once again to this blossoming math blogging community. )