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LGR Interview IIBook review on IMA websiteMathematics with FriendsCarnival of Mathematics 227PubSci TalkInfinitely Irrational Podcast episodesCyprus Mail interview IIChalkdust magazine shortlist 2022Probability gameCarnival of Mathematics 212LGR InterviewLearningconnected blog entryCyprus Mail InterviewChalkdust Reader's choice 2020Chalkdust Magazine ReviewWhat Value is History to Teaching and Learning Mathematics?

In this interview, we explored the role of stories when discussing maths, a mini preview of the upcoming interactive lecture on October 23rd!

Interview in Greek.

Η Βασούλα Χριστοδούλου συνομιλεί με την Εκπαιδευτικό Μαθηματικών, συγγραφέα και καλλιτέχνη Ιωάννα Γεωργίου. Εξερευνήστε ενδιαφέρουσες ιστορίες πίσω από τις μαθηματικές έννοιες και τις ζωές μαθηματικών, αποκαλύπτοντας τις συνδέσεις ματαξύ μαθηματικών, ιστορίας και κοινωνίας.

Book review published directly onto IMA website

**Mircea Pitici (Editor)**

PRINCETON UNIVERSITY PRESS 2022, 320 PAGES

PRICE (PAPERBACK) £20.00 ISBN 978-0-691-22570-8

This book contains articles written in 2020. The editor speaks of the difficulties accessing libraries and resources, something we are all a bit too familiar with. Here I will comment on each of the twenty-six articles selected as the ‘best’ and draw an overall conclusion at the end.

Appropriately enough, the opening article to this volume *Lockdown Mathematics: A Historical Perspective* accounts for historical cases where mathematics was produced in isolation, such as lockdowns or imprisonments (even for noble causes). The article on *Cryptocurrencies: Protocols for Consensus* is very illuminating on permissionless protocols to create cryptocurrencies in a decentralised manner.

The article *Logical Accidents and the Problem of the Inside Corner* discusses how much of the design is now with software and the difficulties that arise. In *Cosmatesque Design and Complex Analysis*, the author discusses how to construct this cosmatesque type of tiling using a branch of complex analysis.

A variety (or algebraic set) is the shape produced by an algebraic equation. The authors of *Nullstellenfont* were looking to create a font where a polynomial equation would create an entire phrase. The *Hyperbolic Flowers* crocheted by the author herself aim to illustrate how hyperbolic planes are formed once the curvature of a construct becomes negative. *Embodied Geometry in Early Modern Theatre* comments on an early modern theatrical play starring 2D shapes, discussing Euclidean definitions of abstract concepts and some torture-related practices.

*Modeling Dynamical Systems for 3D Printing* provides examples on printing chaotic attractors, which are harder to describe and produce than multivariate calculus and geometry. *Scientists Uncover the Universal Geometry of Geology* discusses the amazement the analysis of the shattered rock pieces caused when it was found they average to six faces and eight vertices – almost as if Plato knew earth was made of cubes!

*Bouncing Balls and Quantum Computing* discusses how calculations about idealised billiard balls reveal numbers that increasingly approach an approximation of *π* in a surprising way. *Landmark Computer Science Proof Cascades through Physics and Math* discusses computers becoming more prevalent in mathematical proofs.

The article on *Dark Data*, discusses missing data. Data one does not have is not ignorable. The serious implications of drawing statistical and other conclusions when data is missing are discussed. *Analysis in an Imperfect World* discusses the impact of measurement errors, the repercussions of which are often more serious than one would expect.

*A Headache-Causing Problem* presents a problem where N men (original thesis in 1977 hence the exclusive nature of the crowd, possibly) are called to guess the number on their forehead, following certain rules; is this problem solvable in finite steps or not?

*A Zeroth-Power Is Often a Logarithm Yearning to Be Free* investigates integrating powers of *x* and discusses the exception when *n=-1*. *The Bicycle Paradox* discusses the disparity between a pedal in the lowest position, moving seemingly backwards when the bicycle is moving forwards. *Tricolor Pyramids* discusses triangular formations made with regular hexagons. The challenge is to use three colours to colour all hexagons following certain rules of how to create such puzzles.

*Does Time Really Flow? New Clues Come from a Century-Old Approach to Math* considers how mathematical equations do not make use of the present moment in time but at quantum level, the moment a particle is measured essentially adopts its status, making the present moment a defining moment. The article on *The Role of History in the Study of Mathematics* could come across as slightly opinionated and judgmental of mega-figures in mathematics. Some readers may find this rather surprising. The historical evolution of the Notices of the American Mathematical Society is explored under the lens of anticommunism and racism with some vivid examples, in *“All of These Political Questions”: Anticommunism, Racism, and the Origin of the Notices of the American Mathematics Society*.

A piece on mathematics education *Reasoning as a Mathematical Habit of Mind* discusses how reasoning is rarely the focus of teaching. *Knowing and Teaching Elementary Mathematics – How Are We Doing?* compares aspects of teaching and learning mathematics between US and China. *Tips for Undergraduate Research Supervisors* provides an extensive list of very tangible advice on how to approach the tricky area of supervision. *“The Infinite Is the Chasm in Which Our Thoughts Are Lost”: Reflections on Sophie Germain’s Essays* pays tribute to Sophie Germain’s legacy with some very extensive direct quotes (both in French and English).

The penultimate piece *Who Owns the Theorem?* poses some critical questions about what it means for one to ‘own’ a theorem. The last article is a personal account, entitled *A Close Call: How a Near Failure Propelled Me to Succeed*. It reads almost like a diary entry about what to avoid when preparing for exams, yet how almost failing can sharpen the focus.

Collating twenty-six articles on a variety of maths topics is an achievement in itself. Additionally, under *Notable Writings* at the end of the book is an impressively extended list of references also from 2020. Did the editor go through a couple of hundred articles before deciding on the twenty-six that made the final cut? One would need to go to great lengths to collate such an eclectic selection of topics. Regardless, the collection is wonderfully varied and for all mathematical tastes. I find it highly unlikely that a single individual will find all these articles relevant or ‘best’. The pitch and complexity are most certainly not consistent, but this is not necessarily a criticism as the reader can pick and choose what to read. Will I be buying the next compilations for future years? Possibly, yes!

**Ioanna Georgiou CMathTeach FIMA**

https://ima.org.uk/25092/the-best-writing-on-mathematics-2021/

In our new blog, each episode takes inspiration from dialogues found in TV series. We use the everyday mathematical themes mentioned as our starting point, to explore the fascinating world of mathematics further.

Asuka Young is the wonderful illustrator I collaborated with for "Mathematical Adventures!" and "Peculiar Deaths of Famous Mathematicians" and once more, her illustrations are full of life and bring the mathematical concepts to life!

Check out the episodes so far - once concluded, the maths series with be published as a paperback by Tarquin, in spring 2025.

Welcome to the 227th issue of the Carnival of Mathematics. Thank you to everyone who contributed.

If you would like to host the Carnival yourself, please get in touch!

I hope you will enjoy this issue!

227 was a sitcom running from 1985-1990 that got cancelled because of declining ratings. It currently stands at 7.2 on imdb which is pretty decent. It gets its name from the apartment number central to the story. Not really that exciting.

Now if anyone is interested riding a bus to Bromley North Station or Crystal Palace, 227 holds the answer.

Colour no. 227 is a classic taupe but it is archived for some reason.

Angel 227 is about spiritual knowledge (which numerology might not be). When I did Carnival issue 212, I thought "oh my what are the chances I got an angelic number!?". It seems there are lots of them!

Ok, enough silliness!

227 is a prime number! Yay! It has two factors 1 and 227. It's impossible to split into equal groups of smaller numbers. The previous prime is 223. The next prime is 229 which makes 227 extra special as part of a twin prime pair (which we still do not know if they are infinite). I mean there are more primes in the 220's than in the 20's. That's quite something! 227 is the 49th prime, and the 227th prime is 1433.

Here is the link to the latest episode of math podcast Infinitely Irrational. It is the third of a mini series on Cantor and Multiple Infinities. I've been having so much fun been Nathalie's guest and exploring mathematical (and other) ideas!

Here is an opportunity to go on a virtual maths trip to Stonehenge and contemplate its mathematicality with Tom! (copyright of mathematicality is mine, not Tom's! Ok, I googled it, it is rare but it is not mine either, sadly, but it did occur to me whilst writing this, honest )

Of course, how could it not be fun? In this investigation, Mahdi looks for new ways to calculate pi. It all started with covering a semicircle with triangles, and why wouldn't you!

In this post, Mark looks into colouring the vertices of an icosahedron. Using only three colours, in how many ways can the icosahedron vertices be coloured so two adjacent ones are not the same?

In this post, Kyle delves into the integers and brings various mathematical fields together, exploring similarities or what keeps them further apart.

A brief introduction to the fascinating world of maths from 40,000 years ago! And we could not have survived without it.

The illustrations in Peculiar Deaths of Famous Mathematicians carry an anachronistic object in them - an additional puzzle to the book! Answers in the back. Illustrations by Asuka Young.

Check out not only my books, but also the episodes Recorded as Nathalie's guest on Infinitely Irrational (just below this post, here!)

Journalist Alix Norman gave maths and storytelling a bit of air time: I could not be more grateful!

Check the link below for an interview with insights on the rationale of my second book "Peculiar Deaths of Famous Mathematicians", and the value of storytelling when discussing mathematics.

https://cyprus-mail.com/2023/04/01/the-peculiar-death-of-pythagoras/

Pythagoras's death, illustration by Asuka Young.

Peculiar Deaths of Famous Mathematicians has made the cut for Chalkdust book of the year award. Chalkdust magazine "A magazine for the mathematically curious" has many amazing contributors, many during their research stage of their mathematical studies. Check the magazine itself out for some fun and informative topics!

https://chalkdustmagazine.com/book-of-the-year/chalkdust-book-of-the-year-2022/

It might be old news for many, but I only discovered this dice game over a recent trip. Originally created by Milton Bradley and then acquired by Hasbro (to do all the referencing and copyrighting here - please let me know if I missed someone) this game can have you calculate probabilities until you drop!

Each player gets 13 rounds. In each of those 13 rounds each player is expected to fulfil as many of the combinations on the score sheet as possible. I outline the combinations below. In each round there are five dice that can be rolled up to three times. So you can roll all five dice three times, but in case of some good numbers on the first roll, you can re-roll fewer than five until you get as close to the desirable combination as possible. And this is where the fun with probability starts! You do not need to complete the combinations in the order they appear on the score sheet (that would be practically impossible, or you would end up with few points north of zero).

The 12 combinations you're aiming for are:

1. As many ones as possible

2. As many twos as possible

3. As many threes as possible

4. As many fours as possible

5. As many fives as possible

6. As many sixes as possible

The score for each of these six combinations is calculated by only considering the 1s, 2s, 3s, 4s, 5s, 6s that you achieved in each combination respectively. If in the first six combinations you manage to score at least 63 (neatly achievable by at least three of the desirable value in each of these throws) than you get +35 bonus points.

7. Three of the same - any value and all scores count

8. Four of the same - any value and all scores count

9. Full House - three of the same and two of the same - 25 points

10. Short road - any four consecutive - 30 points

11. Long road - any five consecutive - 40 points

12. Kniffel or Yahtzee - five of the same - 50 points

13. Chance - when your combination does not match anything but you have nice good values and they all count

If on one round you don't succeed in creating any of the combinations, you must forfeit one of the combinations making this impossible to score for that combination even if you roll it later in the game. The best to forfeit are obviously combinations 1 and 2 that do not carry very many points and you can make up for those in different rolls. But then again that's a decision you need to make based on how far in the game you are and what are the remaining chances of getting at least 63 points in the first three hence the +35 bonus.

The 212th Carnival of Mathematics is here! This monthly blog is organised and run by the https://aperiodical.com/ and I'm excited to be hosting for February 2023; here are some new fab mathsy stuff!

Not many numbers enjoy the notoriety of 212, and I’m only finding out by coincidence (hosting the specific issue etc).

The song “212” by Azealia Banks has been played over 2*10^8 on Spotify, the number is part of her childhood neighbourhood area code – please do not take this as condoning to the language in the lyrics.

Apparently, it is also the angel number that gives guidance and helps you make your dreams come true when you *see *it. So, dear readers, from the bottom of my heart: 212, 212, 212, …, 212, …

212 is also a perfume by Carolina Herrera launched in 1997 but would have liked it better if it launched in 2012 (zeros do not count). TfL bus 212 goes between St James Street Station and Chingford Station.

Now some real info on 212: a composite number equal to 2*2*53, its proper divisors add to 166 hence a deficient number (shame).

Math1089 is not quite as obsessed with 212, but with a different interesting number: https://math1089.in/2023/01/18/mathematical-beauties-of-the-number-76923/

For fans of set theory and its marvels, https://www.quantamagazine.org/long-out-of-math-an-ai-programmer-cracks-a-pure-math-problem-20230103/

Check this great thread full of fun ideas: https://mathstodon.xyz/@christianp/109618963869480507

From Euclid to telescopes, geometry is great! Here is a super video with Matt Parker: https://www.youtube.com/watch?v=os0a5au_3Mo

If interested in card tricks, here is one to try: https://www.youtube.com/watch?v=q0RtYl1WjtM

For the teacher colleagues out there – and their students of course, Alpha Beta Maths released quite a few educational videos in January, check the one on simultaneous equations here: https://www.youtube.com/watch?v=cdF_zXH-11k

Resourcaholic has added a review on a new book by Craig Barton, you can read it here https://www.resourceaholic.com/

A couple of new episodes on the podcasts *numberphile *and *the art of mathematics*. Check them out here: https://www.numberphile.com/podcast/michael-merrifield and https://anchor.fm/the-art-of-mathematics

Check out a calculator’s anniversary edition! http://edspi31415.blogspot.com/2023/01/retro-review-hewlett-packard-hp-14b.html

A confusing word problem made its way in a newspaper – see what you think https://www.dailymail.co.uk/femail/parenting/article-11677671/Parents-solve-confusing-Year-Five-maths-homework-question-guess-answer.html

A review of the year in “math” by quantamagazine can be found here: https://www.quantamagazine.org/the-biggest-math-breakthroughs-in-2022-20221222/

And of course, it wouldn’t be a happy new year without the prime minister’s announcement that maths education should continue at least until the age of 18; hurray! https://www.bbc.co.uk/news/uk-politics-64158179

Pythagoras asking the questions

Illustration by Asuka Young

This is the audio from my interview to Yiannis Ioannou at LGR where I talk about my work in mathematics education and the rationale behind my two (so far) books.

The only catch is you need to understand Greek!

Click below to see my guest blog entry at learningconnected

https://learningconnected.medium.com/the-power-of-stories-in-learning-mathematics-65e20b4910c9

Here is a link to my interview to Alix Norman, a former colleague and journalist at Cyprus Mail

https://cyprus-mail.com/2021/03/20/new-book-tells-the-tales-of-maths/

The Chalkdust Magazine Book of the Year award 2020 went to "Molly and the Mathematical Mystery" but the Reader's choice award went to "Mathematical Adventures!"!

Here's details and more information https://chalkdustmagazine.com/blog/book-of-the-year-2020/

Chalkdust reader's choice 2020

Chalkdust magazine is a fun and informative magazine for the *mathematically curious*. "Mathematical Adventures!" was shortlisted for their book of the year 2020 award. We were over the moon, an acknowledgment of the love we poured into creating our first book. Check our the review and find out more about Chalkdust magazine itself here: https://chalkdustmagazine.com/blog/mathematical-adventures/

Sending good wishes for the new year

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