## Carnival of Mathematics #128

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.