Carnival of Mathematics 129

Published by Ganit Charcha | Category - Math Events | 2015-12-16 07:36:24

We are glad to host the $129$th Carnival of Mathematics in December $2015$ after last months Carnival of Mathematics 128  by Mike at  Walking Randomly. Carnival of Mathematics is a monthly blogging round up that is organised by The Aperiodical. We choose to host $129$th Carnival in December because $22$nd of this month is celebrated as National Mathematics Day of India. Indian legendary Mathematician Srinivasa Ramanujan was born on $22$nd December $1887$. In order to recognize his immense contribution towards Mathematics the Government of India has declared Ramanujan's birthday to be celebrated every year as the National Mathematics Day of India. $22$nd December $2015$ is the $129$th $22$nd December starting from Ramanujan's birth year, $1887$. Is not this a nice coincidence?

Adhering to tradition, let us first take a look into some beautiful facts about number $129$.
We start with a crazy sequential representation of $129$ written in terms of $1$ to $9$ in increasing as well as decreasing order (taken from http://arxiv.org/abs/1302.1479).$$129 = 12.3 + 4 + 5 + 67 + 8 + 9 = 9.8 + 7.6 + 5 + 4 + 3 + 2 + 1$$$129$ is the sum of first ten prime numbers, i.e., $129 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29$. $129 = 3.43$ is a semiprime ( a natural number that has only two prime factors, not necessarily distinct) and interestingly enough $A001358(43) =129$, where the description of $A001358$ can be found here {https://oeis.org/A001358}. That means $129$ is the $43$-rd simeprime where $43$ itself is a factor of $129$.

Number $129$ has the following single representations (http://rgmia.org/papers/v18/v18a73.pdf).$$129 = ((aa + a) × aa/a - a - a - a)/a,$$ where $a \in {1, 2, 3, 4, 5, 6, 7, 8, 9}$.

$129$ is a Happy Number. Start with any number. Then square the digits of the number and add them together to form a new number. Take the new number, square its digits and add them together. We continue this procedure until the number either equals 1 or it loops endlessly in a cycle which does not contain 1. If the process ends by hitting eventually number 1, then the starting number is called a Happy Number. For $129$, we have $1^{2} + 2^{2} + 9^{2} = 86$ followed by $8^{2} + 6^{2} = 100$. The number $100$ finally yields $1$ on repeating the procedure.

$129$ can be expressed as sum of three squares in four different ways and it is the smallest number with this property.$$129 = 11^{2} + 2^{2} + 2^{2} = 10^{2} + 5^{2} + 2^{2} = 8^{2} + 8^{2} + 1^{2} = 8^{2} + 7^{2} + 4^{2}$$Lastly, $129$ is neither a pretty wild narcissistic number nor its a Friedman number - but its a near miss. It can still be written as an expression using its own digits and involving operations like ($+$, $-$, $x$, $/$, ^, $\sqrt{}$, $!$) where only one digit is repeated twice. For example, $$129 = 1 + 2^{(9-2)} = (1 + 2^{2})! + 9 = (2 + \sqrt{9})! + (9/1)$$
We will now move on to the posts that make up this months carnival and we start with a post which sheds light on Ramanujan's life.

The Man Who Knew Infinity is a terrific film on the life of Ramanujan, which premiered at the Toronto International Film Festival this September. The movie brought this great historical figure to light in a spectacular way. Anthony Bonato shared with us an excellent review of the film Review of The Man Who Knew Infinity  and the aim of the post is to shine a spotlight on the film, and help it gain exposure to bigger audience (not limited to mathphiles).

An enriching article by Marianne Freiberger in Plus magazine titled Ramanujan surprises again and submitted by Debapriyay Mukhopadhyay talks about a recently made fascinating discovery from Ramanujan's manuscript by two mathematicians of Emory University, Ken Ono and Sarah Trebat-Leder.

David Orden's write up Flip me to the moon  in mappingignorance provides a nice overview of results on the notion of edge flip in triangulations and pseudo-triangulations. It also talks about a very interesting open problem: "Is the flip graph of 4-PPTs connected?"

Robert Fourer shared with us a blog post Which Simplex Method Do You Like?  that talks about history and development of computationally practicable simplex method in the early 1950s, leading to some reflections on the divergence of computational practice and pedagogical convention in presenting and applying the simplex method.

An astounding revelation of true meaning of $-\frac{1}{12}$ - the article ASTOUNDING: The true meaning of -1/12  shows us. The infinite series $1 + 2 + 3 + 4 + \ldots$ is divergent and is not equal to $-\frac{1}{12}$ is what this article talks about. This excellent post in Extreme Finitism was forwarded to us by Karma Peny. We would like to add a point here. The mistake of interpreting the sum of the series $1 + 2 + 3 + 4 + \ldots$ as $-\frac{1}{12}$ comes from the mistake of believing that Riemann Zeta function agrees with the Euler Zeta function for -1. But, actually it is not and Riemann Zeta function agrees with the Euler Zeta function for real numbers greater than 1. For more details read the article Infinity or -1/12 in Plus magazine.

Shecky R forwarded to us a link reviewing John Allen Paulos' recent book, "A Numerate Life" and the title of the post is A Life In Math.

The volume of a sphere via Archimedes is an excellent post inspired by the 3d printed model from Thingiverse that talks about the relationship between the volume of a sphere, cylinder, and cone. Along with this Mike Lawler has also shared with us  Our year in Math - a nice expository article that narrates the biggest things in math that crossed his  path this year.

Ilona Vashchyshyn's first blog post  which she wrote as an intern overwhelmed by how far still still have to go as a teacher. It expresses her worries and acceptance of the fact that a teacher will *never* really stop learning, and along with Ilona we also think that this is a post that other interns or new teachers would identify. Ilona Vashchyshyn has shared with us another interesting article. This postindependent, resilient problem solvers. This post would resonate with any teacher (or even parent) who incorporates problem solving into their lessons and, hopefully, push them to be a little less "helpful".

Brian Hayes interesting post  Ramsey Theory in the Dining Room  talks about a nice, intriguing math problem before the onset of holiday party season.

Diane G has forwarded us a nice post titled the  The Grand Hotel posted in Worldwide Center of Mathematics. This is the story of David Hilbert's Grand Hotel - though many versions of this story is available but its genuinely a nice editio is about one of her math club meetings during where she posed the McNugget Frobenius problem to her students. It describes her  internal battle that in one side wants to be "helpful" and the other side of she that wants to develop n of the story. It's a very interesting read and well written.

Brent Yorgey has provided us the link of the first post  MaBloWriMo: The Lucas-Lehmer test  in a 30-post series which he wrote during the month of November. The 30 post series ends in December 1 with the post  MaBloWriMo 30: Cyclic subgroups. Along the way Brent Yorgey gave a thorough careful proof of (one direction of) the Lucas-Lehmer test for Mersenne primes and also covered some introductory group theory.

Matthew Scroggs has directed us to a blog post titled  MENACE: Machine Educable Noughts And Crosses Engine that talks about how a machine is capable of learning to be a better player of Noughts and Crosses (or Tic-Tac-Toe).

We are happy to make a mention of the post  Fun With Math: How To Make A Divergent Infinite Series Converge  written by Kevin Knudson and submitted to us by Augustus Van Dusen. This article is about Kempner series, and nicely shows that modifications of the harmonic series by discarding all terms containing a specified sequence of numbers render the series convergent in the Cauchy sense.

John Cook has shared with us Mathematical alchemy and wrestling. We liked this post as it aims to identify and recognize four tribes of mathematicians.

Katie Steckles has shared with us the post titled "Prime Numbers and the Riemann Hypothesis", Cambridge University Press, and SageMathCloud which provides a glimpse of the book "Prime Numbers and the Riemann Hypothesis" written by Barry Mazur and William Stein.

Lastly, maths on a lighter note and to this goal we would like to make a mention of the following posts.

The post Stuff Math Professors Say will allow for a break from deep thinking about mathematics.
The post  Why the history of maths is also the history of art showcases 10 stunning images revealing the connections between maths and art. Images shown in the post are borrowed from the book "Mathematics and Art: A Cultural History" by Lyn Gamwell.
Climbing Stairs and Keeping Count along the way to stairs climbing has shown all integers can be reduced to their prime factors.
Christmas is just one week away and this year you can choose Mathsy Gifts - a nice compilation to help you select is here http://www.resourceaholic.com/p/mathy-gifts.html.

This brings to an end of this edition of Carnival of Mathematics. Next Carnival of Mathematics  will be hosted by Brian at  Bit Player.