Hello maths fans! Welcome to the 184th Carnival of Mathematics with your host Dr Tom Crawford. After accidentally starting a trend (see Carnival 167) with listing fun facts about the number of the carnival, here are my favourites about the number 184:

• 184 is the natural number following 183 and preceding 185 (thank you Wikipedia)
• 184 is a Tau Number – which means that the number of divisors it has, 8, is also one of those divisors. Divisors of 184: 1, 2, 4, 8, 23, 46, 92, 184.
• 184 is the difference of two square numbers: 25²– 21²
• 184 is the sum of four consecutive prime numbers – what are they? (answer at the bottom of the page)
• 184 is the atomic number of the element Unoctquadium (yet to be discovered)
• 184 is predicted to be a ‘magic number’ of neutrons in Nuclear Physics – a magic number of neutrons (or protons) occurs when all nucleons (both protons and neutrons) are arranged in complete shells within the atomic nucleus. Discovered by Maria Goeppert Mayer in 1948.
• Rule 184 is a one-dimensional cellular automaton rule that can be used for a simple model of traffic flow on a single lane highway, the deposition of particles onto an irregular surface and ballistic annihilation.

Now that’s out of the way, the only place to start the carnival proper is with Chris Smith and his bold/reckless (delete as appropriate) attempt to come up with 50 interesting puzzles during lockdown. You can find them all on the playlist below – a few personal favourites being number 24 number 42 (naturally).

Speaking of the universe and everything in it, AlephJamesA has been writing about Hyperion – one of the many moons of Saturn. It’s egg-like shape gives rise to a chaotic rotation, which is pretty darn cool.

Continuing the theme, The Universe of Discourse tells us about ‘weird constants in math problems’. I’d argue that could be the title of pretty much any maths blog ever written, but here Mark chooses to focus on Monte Carlo methods for finding the expected number and size of continuously filled bins… And that’s not all. Mark’s been keeping himself busy with a double entry into this month’s carnival via a discussion of Taylor versus Maclaurin series, which provides me with the perfect opportunity to share this (from Reddit of course):

Mark is of course not the only one who’s been keeping busy during lockdown, as my student Joe can attest. He decided to build his very own mechanical sine wave machine which draws perfect sine waves by converting circular motion into a wave pattern. Find out how he did it in the video below.

Next up flags. Who doesn’t love a good flag? Oh, just me and Peter Rowlett then… Alovelypuzzle as part of the IMA series asks us whether it’s possible to create 20 unique flags from only 5 coloured strips. Like Mark before him, Peter’s been modelling his behaviour on London buses as he also offers a lovely discussion of the idea of mathematical modelling through the eyes of his young son.

And now onto the month itself. July was yet another bad month of 2020 for many reasons, but losing the great Ronald Graham chief among them. On the Akamai blog, his friend Tom Leighton talks about his life and contributions to the field of mathematics. Further personal stories from RJ Lipton and KW Regan can be found at Godel’s Lost Letter and P=NP. RIP Ron.

July also saw a significant vote in Russia with changes to the constitution clearing the way for Putin to extend his presidential rule until 2036. Props to Arseny Khakhalin for analysing the voter data and finding all kinds of – let’s say ‘mysterious’ – mathematical phenomena…

We have more magic and mystery abound with Comfortably Numbered discussing phantom horses and the Moire Pattern, while Dan McQuillan tells us all about vertex-magic graphs.

Matthew Scroggs tries to cheer us all up by inventing new maths celebration days in the form of approximations to expressions involving famous numbers. Happy 4√2+e-8 Approximation Day everyone! (Find out which date I’m celebrating at the bottom of the page).

For something a little different, head over at the JHI blog, where E.L. Meszaros talks about the authorship conventions of Babylonian mathematical texts and what we can learn from them in today’s academic environment.

Something else to ponder courtesy of Kareem Carr who tells us why 2 + 2 = 5 isn’t as silly as it might first sound when approached from the mindset of a modeller…

And finally, one of my new favourite words: Desarguesian. I’m happy to admit I’ve never heard of it until I read this post from Senia Sheydvasser and now I can’t get enough – non-Desarguesian or otherwise.

A huge thanks as always to Katie and the team at the Aperiodical for organising the carnival, and thanks to you – the readers – for taking part in the monthly mathematical bonanza. Keep rocking maths.

 Answers:

187 = 41 + 43 + 47 + 53

7/19 = 0.36842105263 and 4*root(2) + e – 8 = 0.37513607795…