This is the 182nd edition of the The Carnival of Mathematics, a blog with a rotating cast of authors that summarises all the fun and intriguing bits of maths that the internet has served up in the previous month.
This edition will begin — as has become traditional — with facts about the number of the edition.
However, to celebrate the era of the virtual quiz that we currently find ourselves in, this edition requires readers to spot which of the facts are true.
-The number 182 has three prime factors.
-The number 182 is a ‘square-free’ number: that is, a number that has no square factors.
-The string 182 occurs for the first time in Pi at the 182nd digit (excluding the 3).
-The number 182 is a ‘deficient number’: that is, a number whose proper factors sum to less than the number itself.
-The number 182 is named after an American rock band from the 1990s.
-There are exactly two ways you can take a subset of the factors of 182 and get a sum of 41.
-A rugby sevens pitch has 14 players on it. Let’s imagine that each player shakes hands with every other player (including their own team mates) twice: once at the start of the game, and once at the end of the game. In this situation, a total of 182 handshakes would take place amongst the 14 players on the pitch.
-If I have a table with 14 distinguishable small items on it, there are 182 ways I can order all the small things.
And now for the round-up of interesting maths.
‘Hardmath123’ has been busy learning how to use gradient descent to approximately reverse a Game of Life configuration. They use the method to make a configuration that evolves to resemble none other than John Conway himself, and then go on to pose some questions about symmetry breaking and Turing patterns.
For something more meta, in ‘The Sentimental Formula’ James Arthur celebrates the way mathematics can evoke memories. The Sentimental Formula reminds us to look up occasionally from the doing of mathematics and to consider the place of the discipline in our personal lives (whilst also teaching us how to derive the quadratic formula!).
And if art has sentimental value, why shouldn’t mathematics? If you’re looking for something perfectly in tune with both your mathematical curiosity and artistic appreciation, check out these infinitely many touching circles in one of many beautiful visualisations from Matt Henderson.
I can’t write the words ‘in tune’ without mentioning the mathe-musical triumph of the month (or the year!), Tom Lehrer’s ‘That’s Mathematics’ performed by a group – (what is the collective noun?) – of mathematicians and coordinated by Ed Southall.
Staying with all things lyrical, in ‘To integrate the impossible integral’ John D Cook manages to combine both musicals and integration. John discusses the importance of introducing, at high school level, integrals that are without an elementary closed form, so that students are better prepared to deal with integrals in the messy real world.
Or perhaps you’ve got students (at school or home) who are not yet studying calculus but for whom this delightful sieve of Eratosthenes visualisation (again from Matt Henderson) could work wonders for their understanding of prime numbers.
Equally, for maths students looking to brush up on their matrices/simultaneous equations skills or to improve their understanding of trigonometric functions, Oluwatosin Oluseyi has got you covered with these clear and easy to follow learning resources: https://twitter.com/olutosinbanjo/status/1239886320031408129?s=19
And Sam Blatherwick neatly communicates Euler’s approach to the Basel Problem in punchy tweet form, whilst highlighting the accessibility of this proof to A-Level students.
Away from thinking about the curriculum, Andrew Taylor has made something both educational and amusing out of the car crash that is the UK government’s communication of the Covid-19 alert level.
Finally, those who have become accustomed to estimating lengths in Richard Osmans during this pandemic may enjoy this Twitter thread and blog from John J Sills about other arbitrary objects that routinely find themselves used as units of measurement.
My calorie intake whilst writing this blog has been equivalent to three quarters of a Big Mac and by word count I’ve written at least a two hundredth of a novel, so it feels like time to stop.
Check back at The Aperiodical to find out who is hosting next month’s Carnival of Mathematics.