### Review: Who’s Counting, by John Allen Paulos

We asked guest author Elliott Baxby to take a look at John Allen Paulos’ latest book, Who’s Counting.

Mathematics is an increasingly complex subject, and we are often taught it in an abstract manner. John Allen Paulos delves into the hidden mathematics within everyday life, and illustrates how it permeates everything from politics to pop culture – for example, how game show hosts use mathematics for puzzles like the classic Monty Hall problem.

The book is a collection of essays from Paulos’ ABC News column together with some original new content written for the book, on a huge range of topics from card shuffling and the butterfly effect to error correcting codes and COVID, and even the Bible code. As it’s a collection of separate columns, it doesn’t always flow fluently – I did find myself losing focus on some of the topics covered, particularly ones that didn’t interest me as much. This was mainly down to the content though – the writing style is extremely accessible and at times witty.

The book included some interesting puzzles and questions, which were challenging and engaging, and included solutions to each problem – very helpful for a Saturday night maths challenge! I even showed some to my friends, who at times were truly puzzled. I loved the idea of puzzles being a means of sneaking cleverly designed mathematical problems onto TV game shows. It goes to show maths is everywhere!

I enjoyed the sections on probability and logic as these are topics I’m particularly interested in. One chapter also explored the constant $e$, where it came from and where else it pops up – a very interesting read. It does deserve more attention, as π seems to be the main mathematical constant you hear about, and I appreciated seeing $e$ being explored in more depth.

This book would suit anyone who seeks to see a different side of mathematics – which we aren’t often taught in school – and how it manifests itself in politics and the world around us. That said, it would be better for someone with an A-level mathematics background, as some of the topics could be challenging for a less experienced reader.

It’s mostly enjoyable and has a good depth of knowledge, including questions to test your mind. While I didn’t find all of it completely engaging, there are definitely some points made in the book that I’ll refer back to in the future!

### The Indiana Pi Legislation

This is a guest post by Storm Reinbolt, outlining a historical mathematical incident which almost caused a misdefinition!

π is an irrational number that is equal to 3.1415926535 (to 10 digits). Things could have been different, however, if Dr. Edward J. Goodwin succeeded in passing Indiana Bill No. 246. This bill would have completely changed π and mathematics as a whole.

In 1894, Dr. Goodwin, a physician who dabbled in mathematics, claimed to have solved some of the most complex problems in math. Among these was the problem of squaring the circle, which was proposed to be impossible by the French Academy in 1775. This is impossible due to the fact the area of a circle is $\pi \cdot r^2$, where $r$ is the radius, and the area of a square is $s^2$, where $s$ is the length of each side.

This was proven by Ferdinand von Lindemann in 1882, and is what makes squaring a circle impossible.

In order to square a circle, $\pi \cdot r^2$ must be equal to $s^2$. For example, if $r=1$, we would have $\pi \cdot 1^2 = s^2$, or $\pi = s^2$. This would mean that each side of the square is equal to the square root of π, and since π is transcendental, there’s no algebraic expression that could describe π.

Regardless, Goodwin claimed to have done it, and published his paper to American Mathematical Monthly in 1894. It was gibberish, and no amount of understanding in mathematics would make his work comprehensible. He claimed nine different values of π across his many works, with one claim going as far as $9.2376\ldots$, “the biggest overestimate of π in the history of mathematics” (A History of Pi). When his theories weren’t becoming popular, he decided to take them to the Indiana State Legislature on January 18, 1897.

Goodwin had convinced his state representative, Taylor I. Record, to introduce House Bill 246 (Indiana Bill No. 246). House Bill 246 would make Goodwin’s method of squaring the circle a part of Indiana law. However, those in the legislature either didn’t understand or didn’t even glance at the bill – and the House Committee on Canals decided to pass it. Dr. Goodwin’s ridiculous bill was now headed to the senate.

At the statehouse where the senate took up the bill was Professor Clarence Abiathar Waldo, a mathematics professor from New York. When Waldo heard what the bill was about, he was shocked to discover he was in the middle of a debate on a fundamental principle of mathematics. He decided to intervene and talk to the senators about the repercussions the bill would have on everything mathematics, and was able to stop the bill from passing the second chamber.

After Waldo’s intervention, it was clear to everyone that the people involved in the attempted passing of the bill, including Dr. Goodwin, were all wrong, and it was ridiculous to define mathematical truth by law.

### Carnival of Mathematics 211

The next issue of the Carnival of Mathematics, rounding up blog posts from the months of November and December 2022, is now online at Ganit Charcha.

The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

### Recurring decimals and 1/7

This is a guest post by David Benjamin.

Rational numbers, when written in decimal, either have a terminating string of digits, like $\frac{3}{8}=0.375$, or produce an infinite repeating string: one well-known example is $\frac{1}{7}=0.142857142857142857…$, and for a full list of reciprocals and their decimal strings, the Aperiodical’s own Christian Lawson-Perfect has built a website which generates a full list.

I’ve collected some interesting observations about the patterns generated by the cycles of recurring decimals, and in particular several relating to $\frac{1}{7}$.

### Blockbusters of Interesting Maths

As part of the 24 Hour Maths Game Show which took place at the end of October 2022, our own Christian Lawson-Perfect designed a maths/games crossover gameshow format to end them all – a mashup of hexagon-fighting TV quiz Blockbusters, and his own personal obsession: interesting mathematical factoids. Welcome to Blockbusters of Interesting Maths!

### How to fold and cut a Christmas star

This week and last I hosted a series of public maths talks featuring disabled presenters. I’ll post about how that went later, but for now I just want to share this clip of me filling time spreading Christmas joy.

This is a party trick that Katie Steckles showed me: you can fold a piece of paper and then make a single cut to produce a five-pointed star. I showed how to do it by following the instructions I’d been told, and then recreated the steps just starting from the insight that when you make the cut, all the edges of the shape need to be on top of each other.

Maybe you’ll show someone else how to do it during the Christmas holiday?

This doesn’t only work for stars: there’s a theorem that you can make any polygon by folding and a single cut. Erik Demaine has made a really good page about the theorem, with some examples to print out and links to research papers. Katie can cut out any letter of the alphabet on demand, which is impressive to witness!

### Interview: Coralie Colmez, author of The Irrational Diary of Clara Valentine

We spoke to Coralie Colmez, mathematician and author of Math on Trial, about her genre-busting new Young Adult novel for mathematically minded teenagers: The Irrational Diary of Clara Valentine.