## Archive for the ‘Carnival of Math’ Category

Welcome to the 194th Carnival of Mathematics! I am extremely late in posting this…so late in fact that the 195th edition as already been published!

194 has a few interesting properties. According to its wikipedia entry, 194 is an odious number that is also the smallest Markov number that is neither a Fibonacci number nor a Pell number. It’s the smallest number that can be written as the sum of three squares in five ways and is the number of irreducible representations of the Monster group.

**Micro Visual Proofs – Animated proofs without words**

Proofs without words have been around for a long time. Diagrams that demonstrate that a mathematical statement is ‘obviously’ true. The example that always springs to my mind is the one below that demonstrates that the sum of consecutive odd numbers is a square number.

Such things have appeared in print for years. The books by Nelsen are a wonderful source of many of them and the Mathematical Association of America has a few very nice interactive examples.

Tom Edgar has been working on videos that animate proofs without words for a new YouTube channel called Micro Visual Proofs and submitted the one below for this month’s Carnival of math.

**2.648102… Has anyone seen this constant?**

Peter Cameron has been working on graphs on groups and has come across the constant 2.648102…. In this post he discusses how it turned up and asks if anyone else has come across it. There’s an interesting discussion in the comments section

**Electrostatics and the Gauss–Lucas Theorem**

Insight into mathematical theorems can come from many different places with physics being an extremely common one! Physical problems can be very useful in making even the most abstract concepts more concrete. John Carlos-Baez demonstrates this perfectly in his post Electrostatics and the Gauss-Lucas Theorem

**Mathematics from TikTok**

When the carnival of mathematics first began, it was all about mathematical blogs – a medium that was relatively new at the time. There was something wonderful about seeing mathematicians, scientists, teachers and hobbyists communicating more directly with the world. Internet time moves quickly and there has since been an explosion of interesting mathematical discussion on many other social media platforms — one of these being TikTok.

In this twitter post by Howie Hua, a teacher of math to future elementary school teachers, Howie advertises a TikTok video where he asks ‘What Happens if we add fractions across?’

New TikTok video: What happens if we add fractions across? pic.twitter.com/RDfU7AHYKL

— Howie Hua (@howie_hua) May 21, 2021

**The Mathematigals Show**

Mathematigals is a new YouTube channel that asks explores things like ‘What do broccoli and lightning have in common?’ and The Potato Paradox. In this month’s submission they discuss the source of many a mathematical argument, The Monty Hall Problem. Head over to YouTube to subscribe to their channel and show your support.

**21-card trick explained**

Mathematics is at the foundation of many card tricks and here is Ganit Charcha demonstrating one of them

.

Ganit has several videos on various aspects of mathematics and you can subscribe to his channel to show your support.

**Shock Me Amadeus**

Larissa Fedunik-Hofman of Sydney’s Mathematical Research Institute writes:

“In this profile video of applied mathematician Bronwyn Hajek from the University of South Australia, Hajek describes how she is motivated by the

quest to solve tricky, obscure, unsolved partial differential equations. Hajek will visit the Sydney Mathematical Research Institute in coming

months to collaborate on a project to apply Lie symmetry methods to model biological shocks.

I hope you like this video, which covers her upcoming project and some of the mathematical breakthroughs that Hajek has been involved with in recent years.”

**Chalkdust – A magazine for the mathematically curious**

Robin Whitty submitted this post that celebrates the launch of issue 13 of the Chalkdust magazine which focuses on John Conway, creator of the game of life, among many other things.

Welcome to the 128th Carnival of Mathematics, the latest in a mathematical blogging tradition that’s been ongoing for over 8 years now!

**Facts about 128**

It’s said that every number is interesting and 128 is no exception. 128 is the largest number which is not the sum of distinct squares whereas it is the smallest number n such that dropping the first and the last digit of n leaves its largest prime factor (thanks, Number Gossip).

Wikipedia tells us that it is divisible by the total number of its divisors, making it a refactorable number. Additionally, 128 can be expressed by a combination of its digits with mathematical operators thus 128 = 2^{8 – 1}, making it a Friedman number in base 10.

128 was also the number of kilobytes of memory available in the magnificent computer shown below.

**The Princeton Companion to Applied Mathematics**

I recently received a copy of the The Princeton Companion to Applied Mathematics and it’s just beautiful, definitely recommended as a christmas gift for the maths geek in your life. The companion’s editor, Nick Higham, has written a few blog posts about it – Companion authors speaking about their work, Famous Mathematicians and The Princeton Companion and How to Use The Princeton Companion to Applied Mathematics.

**We have a lot of problems, and that’s a good thing**

‘Diane G’ submitted this advanced knowledge problem — great practice for advanced mathematics. This blog is amazing and posts practice problems every Monday and advanced problems every Wednesday.

**Linear Programming**

Laura Albert McLay of Punk Rock Operations Research (great blog title!) submitted two great posts: Should a football team run or pass? A game theory and linear programming approach and dividing up a large class into discussion sections using integer programming

Francisco Yuraszeck submitted 10 Things You need to know about Simplex Method saying ‘*This article is about the basics concepts of Linear Programming and Simplex Method for beginers in Operations Research.*‘

**Computation**

Stuart Mumford demonstrates various ways of computing the first 10,000 numbers in the Fibonacci Sequence using Python — and some are **much** faster than others. Laurent Gatto followed up with a version in R.

Cleve Moler, the original developer of MATLAB, looks at three algorithms for finding a zero of a function of a real variable:

- Zeroin, Part 1: Dekker’s Algorithm
- Zeroin, Part 2: Brent’s Version
- Zeroin, Part 3: MATLAB Zero Finder, FZERO

Michael Trott of Wolfram Research looks at Aspect Ratios in Art: What Is Better Than Being Golden? Being Plastic, Rooted, or Just Rational? Investigating Aspect Ratios of Old vs. Modern Paintings

Andrew Collier explores Fourier Techniques in the Julia programming language.

**Optimisation**

The Numerical Algorithm Groups’s John Muddle looks at solving The Travelling Rugby Fan Problem.

Robert Fourer gives us two articles on Quadratic Optimization Mysteries: Part 1 and Part2. These are posts concerned with computational aspects of mathematical optimization, and specifically with the unexpected behavior of large-scale optimization algorithms when presented with several related quadratic problems.

**Why Was 5 x 3 = 5 + 5 + 5 Marked Wrong**

This image went viral recently

It generated a LOT of discussion. Brett Berry takes a closer look in Why Was 5 x 3 = 5 + 5 + 5 Marked Wrong.

**Misc**

Katie Steckles submitted an article that analyses the different visual themes explored by M.C. Escher in his artwork

Shecky R writes about our curious fascination with eccentric and top-notch mathematicians in Pursuing Alexander.

Brian Hayes has been Pumping the Primes and asks “Should we be surprised that a simple arithmetic procedure–two additions, a gcd, and an equality test–can pump out an endless stream of pure primality?”

**Next time**

Carnival of Maths #129 will be delivered by the team at Ganit Charcha. Head over to the main carnival website for more details.

The Carnival of Mathematics has become something of a tradition in the mathematics blogging community. It’s been going since 2007 which makes it an old-timer in internet terms. The carnival is hosted by a different blogger every month and next month it’s my turn again! If you’d like to see what one of my Carnival of Maths blog posts looks like, take a look at how I did it in the past.

I’ll be hosting carnival number 128 so if you’d like your mathematics blog article featured please send me a submission using this form.

Welcome to the rather delayed Carnival of Mathematics for July. This is the 113th edition of the mathematical blogging tradition that’s organised by Katie and company over at The Aperiodical.

**Number Trivia and a challenge**

Long held tradition dictates that I find something interesting about this month’s edition number – 113 – and I turn to Number Gossip for help. It comes up with 3 very nice little prime tidbits:

- 113 is the smallest three-digit permutable prime
- 113 is the smallest three-digit Unholey prime: such primes do not have holes in their digits
- 113 is the smallest three-digit prime whose product and sum of digits is prime

**Walking Randomly Challenge**: Prove the above using the programming language of your choice and post in the comments section. Here’s a demonstration of the first statement using Mathematica.

(*Returns true if num is a permutable prime*) permutePrimeQ[num_] := AllTrue[PrimeQ[Map[FromDigits, Permutations[IntegerDigits[num]]]], TrueQ] (*prints all permutable primes from 1 to 1000*) Do[ If[permutePrimeQ[x], Print[x]] , {x, 1, 1000} ] 2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 199 311 337 373 733 919 991

**On with the show**

**Mathematical software blogs**

A math carnival wouldn’t be a WalkingRandomly math carnival without some focus on mathematical software blogs. Loren of The Art of MATLAB brings us Analyzing Fitness Data from Wearable Devices in MATLAB which is a guest post by Toshi Takeuchi. The new computational programming language on the block is Julia and the Julia blog contains videos and code on mathematical Optimization in Julia. The Wolfram Blog has a video on how to Create Escher-Inspired art with Mathematica (Don’t forget that Mathematica can be had for free for the Raspberry Pi).

Sage is a free, open-source alternative to Mathematica, Maple and MATLAB and the SageMath blog recently published SageMathCloud — history and status. The Numerical Algorithms Blog, on the other hand, brings us Testing Matrix Functions Using Identities. Efficient linear algebra routines form one of the cornerstones of modern scientific computing and July saw the publication of a tutorial on how to write your own, super-fast Matrix-Matrix Multiply routine.

**Stamps, Making Change and Dealing Cards**

When was the last time you used a postage stamp? Even if it was a long time ago, you may have held in your hands a strip of stamps. Maybe you have even tried to fold it into a stack, one stamp wide, so that the strip was easier to store. Have you ever wondered how many ways there are to do so? This post reviews a recent research survey about the topic.

How many ways can you make change for a dollar? This post gives a Lisp program that solves the problem and an analytical solution based on generating functions.

Over at The Aperiodical, home of the math carnival, Dave Wilding has been Discovering Integer Sequences by dealing cards.

**Ninjas, Lord Voldemort and Hairy Hay Balls**

Colin Beveridge has written a delightful follow-up to Pat Ballew’s post which featured in CoM112 – Trigonometric Trick Secrets of the Mathematica Ninja.

Ben of Math with Bad Drawings fame has written a highly readable rant about a bit of syllabus design which will resonate with anyone teaching (or learning) mathematics in The Voldemort of Calculus Classes.

New math blogger, Grace, recently had an experience in which her math education intersected with her everyday life in Hay Ball Meets the Hairy Ball Theorem.

**Tweeting bots, 3D Printed Geometry and Hair ties**

*(/begin shameless plug)* I spend a lot of time on twitter posting as @walkingrandomly *(/end shameless plug)* and have discovered quite a few mathematical twitter bots in my time. Evelyn Lamb has discovered many many more and has posted reviews of them all over at Roots of Unity.

James Tanton posts fun problems on twitter all the time. One particular problem caught the attention of Mike Lawler because of how 3D printing could help younger children see the geometry.

If you’ve ever wondered what a 120-cell would look like if it were made out of hair ties, wonder no longer because Andrea Hawksley has made one – Hair Tie 120-Cell (By the way, hold your mouse of the title of her blog – it’s cool!)

**More Ninjas, Dots and Mandelbrots**.

A round-up of fun stuff from Colin Beveridge’s “Flying Colours Maths” – a kind of @icecolbeveridge carnival for Mathematics Carnival.

Have you ever wondered what mathematics is behind those pretty Mandelbrot posters that are all over the place? Find out over at Grey Matters: Blog – Mandelbrot Set: What Exactly Are We Looking At, Anyway?

Did you know that dots have power? To see how much power, check out Keith Devlin’s article The Power of Dots.

**Football, drugs and underwear**

Since I’m not a big fan of football at the best of times, the football world cup is a distant memory for me (England’s dismal performance didn’t help much either). Fortunately, there’s more than one way to enjoy a world cup and Maxwell’s Demon and The Guardian helped me enjoy it in a data science way: How shocking was Brazil’s 7-1 defeat, mathematically speaking? and Data Visualization, From The World Cup To Drugs In Arkansas.

At this time of year, many of us turn our thoughts to vacations. If you are a math geek, you owe it to yourself to optimise your underwear and pack like a nerd.

**Puzzles, Games and playing like a mathmo**

When I’m on vacation, I often take a notebook with me so I can do a little mathematics during downtime. My wife and friends find this extremely odd behaviour because mathematics looks like hard work to them..in short, they don’t know how to play like a mathematician.

My job at The University of Manchester is wonderful because it often feels like I am being paid to solve puzzles. While on vacation, however, I have to find some unpaid puzzles to solve and this concentric circles puzzle is an example of one thats fun to solve.

I think that one of the best ways to learn is through play and games and, in a new post over at Math Frolic, a Li’l Game From Martin Gardner introduces mathematical “isomorphism.”

**Cartoons and Limits**

Mathematics is everywhere, it’s even in the voice bubbles used in web comics! As an added bonus, this blog post contains a little Python programming too.

Next up, we have Part 2 of Bressoud’s masterful investigation (Part I featured in Carnival 112) of how students understand limits.

**Resources, Exams and Books**

Colleen Young brings us a great set of Standard Form Resources.

Patrick Honner continues his long-running evaluation of New York State math Regents exams, the high school required exams there. In this post, he looks at a multiple choice question that asks the student to identify the graph of an “absolute value equation”.

The Maths Book Club gives details of their most anticipated maths books for the rest of 2014.

**Bad Mnemonics and a Dislike of Mathematics **

Andrea Hawklsey muses on why some people dislike mathematics when they have interests that suggest they should. Perhaps it has something to do with poorly executed mnemonics when students are taught mathematics, or perhaps its just because they had dull math teachers? Most of my math teachers were awesome and I’ve always felt that this was a major factor in me enjoying the subject.

**Skirts, Snow globes and Mathematical Mind Hacking **

This edition of the carnival is in danger of becoming the Carnival of Andrea Hawksley since so many of her great posts were submitted! In one of her July posts, she manages to combine fashion and hyperbolic geometry – which is quite a feat!

The author of cavmaths has been musing over the dynamics governing snow globes. Can anyone help out?

Hacking your mind sounds like it might be dangerous but it turns out that it’s really quite safe. Head over to Moebius Noodles to see an example of a mathematical mind hack.

**That’s all folks**

Thanks to Katie for inviting me to host this month’s carnival, thanks to everyone for submitting so many great articles and thanks to you for reading. Carnival #114 will be hosted over at SquareCirclez.

It’s been quite some time since I hosted a Carnival of Mathematics with the last one being #90 back in September 2012. I am very pleased to announce that I’ll be hosting #113 next month and am currently accepting articles. If you’ve written a mathematical blog post recently and would like to give it more exposure, send in a submission.

Welcome to the 90th edition of the Carnival of Mathematics and the first one hosted by me since I handed over the administrative reigns to the good people of aperiodical. The CoM is a great way to read about and promote mathematical blogging and has been running for over 5 years. Hosted on a different blog each month, it covers the entire mathematical spectrum from simple mucking around with numbers right up to cutting edge research.

Writers can submit their own posts for inclusion in a carnival if they like and anyone can submit any mathy post that they’ve found interesting– ideally, something written over the last month or so to keep it fresh.

If you want to keep up with the CoM, head over to its twitter feed or the dedicated page at aperiodical.

**Trivia**

Carnival tradition dictates that I post some trivia about this month’s edition number. Here’s what I came up with for 90:

- 90 is the only number that is the sum of its digits plus the squares of its digits (via NumberGossip)
- 90 is a Harshad number in base 10. It is also a Perrin Number, a pronic number, a unitary perfect number and a semi perfect number.
- 90 is the smallest number that has six representations as a sum of four positive squares (via Wolfram Alpha)

**Neat Stuff**

- Matthew Handy explains how researchers at MIT used geometric series to solve an economic problem in Zeno’s Facebook Page.
- Carnival regular, Pat Ballew tells us about a nice connection between numeric frieze patterns and triangulating polygons.
- Ethan Brown, a thirteen-year-old “Mathemagician” and the author of the blog coolmathstuff.com brings us Probability, The Number e, and Magic all in one

**Computation**

- The Numerical Algorithms Group (NAG) discusses Linear Quantile Regression, a new feature in the latest version of their software.
- Samir Kahn has been Modelling Flow Intertia in Three Couple Liquid Tanks using Maple.
- Cleve Moler, inventor of MATLAB, has written two posts on Conway’s Game of Life (part 1, part 2)

**Puzzles and Games
**

- Shecky R brings us Mind Wrenching – A self-referential logic puzzle that will give your brain cells a workout.
- Brent Yorgey has been visualizing winning strategies for “nim-like” games and says
*‘This is a post about visualizing winning strategies for certain games where players take turns removing counters from two piles. The games make for fun games to actually play, and analyzing them can get quite interesting!’*

**Funnies**

- The xkcd comic shows how pointless the phrase ‘We are the fastest growing [whatever]’ is
- Mark Dominus offers a koan on the Consistency of the Peano Axioms.

**Art and Mathematics
**

- Egan Chernoff sent in Alternative Base Representation saying
*‘I look forward to your critiques of my latest piece’* - Gianluigi Filippelli gives us Poincaré, Einstein and Picasso: children of time and says
*‘Following an article by Arthur I. Miller on the Guardian, I try to tell the possible connections between cubism, mathematics and relativity.’* - Gianluigi continues his cultural theme with a look at some mathematical poems recently published in Nature in The day of mathematical poetry.

**Books**

- Shiva Kintali has reviewed a couple of books – Matching Theory by Laszlo Lovasz and Elements of Automata Theory by Jacques Sakarovitch.

**Tricks and Tactics**

- John D Cook gives us Binomial Coefficient Trick

**Topology**

- Mark Dominus of The Universe of Discourse gives us three posts this month: A two parter on topology and set theory (Click here for part 1 and here for part 2).

**Teaching**

- Dan McQuillan gives us On Trigonometric Nostalgia and says
*‘This is a post about fostering a problem-solving mentality in a world where we do not even understand how our own tools work. It superimposes our nostalgia for the world we used to know with our innate curiosity, which still exists. Basic trigonometry is still fun and still relevant. Indeed, one can always ask questions and calculate!’* - Frederick Koh takes on the dot product in Understanding MATTERS (7) saying ‘T
*his dot product concept involving parallel vector planes is rather fundamental, yet a handful of my students are unable to figure out how things exactly work. Hence I have decided to pen this detailed explanation in the hope that it will benefit not just my charges, but other math learners as well.’* - Augustus Van Dusen has written the first in an upcoming series of posts that will prove properties of logarthmic and exponential functions. Augustus says
*‘This particular post will focus on the properties of logarithmic functions of real variables. Students in advanced placement calculus in high school and beginning college students who are not math majors are the intended audience.’*

**Comment**

- Peter Rowlett asks does mathematics have a culture of historical inaccuracy?
- Mike Thayer submitted his article Tired of playing defense saying
*‘These are my thoughts on the Andrew Hacker NY Times article from July, and the Roger Schank Washington Post article from earlier this week.It is my defense of teaching algebra…’* - Egan Chernoff submits Bill, you had me at “arithmetic” and asks
*‘how do other people feel about the phrase “let’s do the math.” ‘*

**Not the only game in town**

The Carnival of Mathematics isn’t the only mathematical blog carnival that’s doing the tour. There’s also the fantastic monthly Math Teachers at Play.

**End**

That’s it for the 90th Edition. Past editions written by me include 80, 76, 74 and 73 among others. For future editions keep an eye on @carnivalofmath and aperiodical.com

I’m hosting the 90th Carnival of Mathematics very soon. If you have written (or read) a mathematics blog article over the last month and want to give it more attention, why not make a submission? The deadline for submissions is 10th September.

For the last two years or so I have been doing the administration for The Carnival of Mathematics (CoM) and have had a lot of fun doing so. I first took over for carnival 59 (written by Jason Dyer and hosted over at NumberWarrior) and did the admin right up until number 84 which was published back in December 2011 by Guillermo Bautista (see here and here for some history).

Recently, however, I have struggled to find the time to give the CoM the attention it deserves and so it is time to hand over the baton. Thankfully, some very able hands have taken it from me and I am happy to announce that Peter Rowlett, Katie Steckles and Christian Perfect will be taking care of business from now on. Submissions for Carnival 85 are already open.

I’ll still be around, blogging as usual here at WalkingRandomly and hosting the occasional Carnival myself but the carnival is now being cared for by the next generation. Submit something and give them a great welcome.

Welcome to the heavily delayed 80th Carnival of Mathematics. Apparently, 80 is the smallest number with exactly 7 representations as a sum of three distinct primes. Head over to Wolfram Alpha to find them. 80 is also the smallest number that is diminished by taking its sum of letters (writing out its English name and adding the letters using a=1, b=2, c=3, …) – EIGHTY = 5+9+7+8+20+25 = 74 (Thanks Number Gossip).

Over at The Endeavour, John Cook discusses the principle of the single big jump (complete with SAGE notebooks) where he demonstrates that ‘your total progress is about as good as the progress on your best shot’…but only if the distribution is right.

Denise asks “What was it really like to work and think in Roman numerals, and then to suddenly learn the new way of calculating? Find out with these new books about math history.” in Fibonacci Puzzle. She is also running a competition which will be ending very soon so you’ll need to hurry if you want to enter.

Guillermo Bautista discusses origami in Paper Folding: Locating the square root of a number on the number line while Gianluigi Filippelli explains how some researchers found a solution to a computational problem using a biological network.

David R. Wetzel gives us Saving the Sports Complex Algebra Project in an effort to better engage math students while Alexander Bogomolny brings us a whole host of engaging math activities for the summer break and Pat Ballew introduces a Sweet Geometry Challenge.

I came across a couple of interesting articles about Markov Chain Monte Carlo (MCMC) simulations this month. The first is from John Cook, Markov Chains don’t converge while the second is by Danny Tarlow, Testing Intuitions about Markov Chain Monte Carlo: Do I have a bug?

Matt Springer brings us Spherical Waves and the Hairy Ball Theorem (below)

Peter Rowlett of Travels in a Mathematical World fame recently had a paper published in Nature about the Unplanned Impact of Mathematics where he talks about how it can take decades, or even centuries, before research in pure mathematics can find applications in science and technology. For example, quaternions, a 19th century discovery which seemed to have no practical value, have turned out to be invaluable to the 21st century computer games industry! Something for the bean-counters to bear in mind when they obsess over short term impact factors of research.

Over at Futility Closet, we have a fun problem called School Reform.

Terence Tao gives us a geometric proof of the impossibility of angle trisection by straightedge and compass while the Geometry and the imagination blog discusses Rotation numbers and the Jankins-Neumann ziggurat.

Several people have been discussing recent changes in EPSRC (The UK’s main UK government agency for funding research and training in engineering and the physical sciences) including Timothy Gowers (A message from our sponsors), Burt Totaro (EPSRC dirigisme) and Paul Glendinning (Responding to EPSRC’s Shaping Capability Agenda).

Finally, one of my favourite mathematical websites is MathPuzzle.com. Written by Ed Pegg Jr, it is possibly the best online resource for recreational mathematics you can find. Go and take a look, you’ll be very glad you did.

That’s it for this month. The next Carnival of Math will be over at Wild About Math on 2nd September and you can submit articles using the carnival submission form. If you can’t wait until then, head over to I Hope This Old Train Breaks Down for the Math Teachers at Play carnival on August 19th. If you are new to the math carnivals and are wondering what’s going on then take a look at my introduction to mathematics carnivals.

**Follow the Carnival of Math on Twitter: @Carnivalofmath** This is also the best way of reaching me if you’d like to be a future host for the carnival.

I do the administration for the Carnival of Mathematics and am very happy to announce that the 77th edition has been published over at Jost a Mon. If you are unsure what a Math carnival is then check out my introductory article or just read some past editions from either the Carnival of Math itself or its sister publication, Math Teachers at Play which is run by Denis of Let’s Play Math fame.

The next Carnival of Math is scheduled to be hosted over at JimWilder.com and the submission form for articles is open now. If you’d like to host a future carnival of math on your blog or website then please contact me for further details.