Hey! This is the 120th Carnival of Mathematics! The Carnival of Mathematics is organized by the nice folks at The Aperiodical.

As per tradition, let me start with some facts about the number 120, and good heavens, where do I start?

• If you say “5” really loudly, you’re really saying 120.
• 120 happens to be an abundant number, since its proper divisors are 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60 and their sum is 240, which is twice 120!
• If we permit leading zeros, then 012, 102, 120, 210 are numbers created from the permutation of the digits of 120 and which happen to be abundant numbers.
• 120 is not a Fibonacci number (a negative fact!).
• However, the 120th Fibonacci number is 5358359254990966640871840.
• \(120^{120}\) is a 250-digit number with 120 trailing zeros (is that really a surprise?).
• \(11 \times 11 – 1 = 120\) which is fun because one was the only digit used on the left-hand side. But alas, I suppose I could done this just as so via \(1 + 1 + \cdots + 1 = 120\) where the left-hand side consists of 120, ones.
• \(120 \pm 7\) are both primes.
• \(120 \pm 11\) are both primes.
• \(120 \pm 19\) are both primes.
• \(59 + 61 = 120\) (twin primes on the left-hand side), \(120 + 59 = 179\) (prime! on the right-hand side), \(120 + 61 = 181\) (also prime on the right-hand side).
• 120 is a pretty fascinating number and Wikipedia kills it.

Now on to the blogs!

Blogs

The Science Pundit discusses calculating Pi in celebration of the “the greatest Pi Day of the century”.

Tom Bennison (@DrBennison) also winds through the history of calculating Pi.

Continuing with Pi Day, we have Don’t Recite Digits to Celebrate Pi. Recite Its Continued Fraction Instead.” from Evelyn J. Lamb (@evelynjlamb).

Speaking of continued fractions … John D. Cook (@JohnDCook) demonstrates empirically computing Khinchin’s constant. The convergence is rather slow. It’s something I’ve been meaning to fiddle with. This is quite a good article!

Next, from Tom Bennison is a little Geogebra. He also gives links to the original Geogebra files for anyone curious.

John D. Cook gives an answer to “Why Isn’t Everything Normally Distributed?”. In his own words, “The Central Limit Theorem explains why many things have a normal (Gaussian) distribution. But why don’t more things have this distribution?” This is a nice read!

Speaking of distributions … shuffling \(N\) elements can be tricky business, but what if the shuffling is too good? What about that shuffling algorithm in your music player? Read about it here in this article on BBC.

Stephen Cavadino (@srcav) does a little finance in his Blaise of Glory article.

Here’s an interesting story of a radio debate that Nira Chamberlain (@ch_nira) had about the usefulness and beauty (among other things) in mathematics.

Evelyn J. Lamb shares a post by one of her math history students on the 3010tangents blog. This post delves into the math history behind imaginary numbers as well as the intrigue in the Tartaglia / Cardano saga.

Tanya Khovanova has a punful gripe about a paper submission about nothing.

From the priceonomics blog we have this recounting of The Time Everyone “Corrected” The World’s Smartest Woman. What’s personally interesting about this event is that I actually remember seeing this unfold as a kid. I was a bit too young to understand the subtleties but the Monty Hall problem always stayed in the back of my mind. Then when I was old enough to process the problem, I programmed it as one of my first programming exercises and saw why it was better to switch doors.

Last but not least, this article from the Wait But Why blog is brilliant. The discussion is about “Your Family: Past, Present, and Future” and what one’s family tree will look like and what one’s family tree looked like. How far back do we have to go before we start to get a little weirded out by all the incest? A fun new term I learned — “pedigree collapse”.

Well, that wraps it up for Carnival #120. Carnival #121 is at Life Through A Mathematician’s Eyes. And here’s a link to the Pi Day post there!