Welcome to the 156th edition of Carnival of Mathematics!
Welcome to the 156th edition of Carnival of Mathematics, meta-hosted by the remarkable aperiodical.com.
What is interesting about 156? Well, it doesn't start with the digit 4.
OK, I'm cheating and pitching straight in: 156=13×12 and the 13-times table doesn't have entries starting with digit 4 until it necessarily does. And Christian Lawson-Perfect has turned this into a cute question, Exactly how bad is the 13 times table? giving rise to a cute conjecture and a cute integer sequence which begins 9, 45, 27, 23, 18, ... . It appears as sequence number 249067 in the Online Encyclopedia of Integer Sequences. There's an intriguing story about how modern mathematics is done here: CLP apparently posted his sequence at OEIS several years ago. The conjecture was suggested by OEIS editor Charles R Greathouse IV. Subsequently it was tackled by two different UK Mathsjam groups. CLP's "Exactly how bad..." update appeared at aperiodical.com on 15th March. Did this inspire CRG IV? Because he adds to the OEIS entry on March 17th an announcement that the conjecture is correct!
In other news, OEIS had reached 3×105 entries at the time of another CLP@Aperiodical submission to Carnival. And at the time of writing another 2400 sequences have been checked and posted—OEIS truely is an astonishing resource!
But one which can make you lazy... a Carnival submission from Danesh Forouhari simply asks : 1/3, 1, 1/4, 1, 1/5, ?,?. My lazy reaction to 'what comes next' puzzles is immediately to ask OEIS. In this case the five denominators produced 135 answers (but mostly not beginning with 3, unfortunately at present this is a search that can only be done by downloading all 3.2×10^5 sequences and searching manually). Anyway perhaps Danesh would accept 1/3, 1, 1/4, 1, 1/5, 1/3, 1/3 from the decimal expansion of 1/3×√(120-18×√3) which is sequence A221185?
Harking back to 13, for those who read French, this Blogdemaths submission about John Conway's base 13-based counterexample to the converse of the intermediate value theorem is excellent. Yet another amazing thing I'd never heard of! (Although there's a whole wiki page about it...) Another example of Conway's genius for inventing the uncanny and then demonstrating uncanny mathematical control over it. And a counterexample also to my conviction that number base tricks (social media is awash with them) are not mathematically interesting. Another counterexample is a base 10 thing uncovered by the wonderfully wide-ranging John D Cook in Squared digit sum.
March boasts an important date and an important date: March 14th is Pi Day and March 8th is International Women's Day. I'd hoped to get blog submissions to mark the 8th but it didn't quite happen. Still, there was an inspirational edition of a sister carnival, Denise Gaskin's Let's Play Math hosting the 115th edition of the Playful Math Education Blog Carnival, honouring Women's History Month by inserting many pictures and quotes from female mathematicians.
Evelyn J. Lamb and Kevin Knudson's podcast series My Favorite Theorem is another superb source of quotes from female mathematicians: of fifteen theorems featured so far eight are chosen by women. The March post didn't happen to be—Federico Ardila on matroids, fascinating—but that's fine, there was a 50% chance it could have been.
[[Update: What I should've been aware of even though it wasn't submitted to Carnival was that My Favorite Theorem did actually post specifically on 8th March! ]]
Another Aperiodical post will serve as a tribute to March 8th and (sort of) 14th: female mathematician Katie Steckles has been running π km every day in March for Sport Relief (...she did it! You can, at the time of writing, still donate here. Congratulations also because she has recently for being announced by the London Mathematical Society as one of its popular lecturers for 2018). Nira Chamberlain gives us, indirectly, a worthy contribution for 8th March with this on the work of Shuri, princess of Wakanda in the film Black Panther. Shuri is a black female STEM icon. Chamberlain, as it happens, is well-qualified to explore the STEM involved and finds it plausible. Consolidating a role model, even a fictional one, is a valuable thing to do, I believe.
Katie Steckles has another contribution this month about a game called "No More Women". Sounds rather anti-March 8th? Not at all, it's an excuse for a roam around various things set-theoretical.
As for March 14th, actually there wasn't really anything in the Carnival postbag specifically for Pi Day either but the occasion gets a nod in a charming and thought-provoking poem e to thee x by Zoe Griffiths for Chalkdust magazine. It appears in the seventh edition of the magazine, announced in another Chalkdust submission. Chalkdust is something of a phenomenon going, in three years, from nothing to established part of the mathematical landscape, second in the UK only to the mighty Plus, which has been going for more than twenty years.
Poor Pi Day, lost in the long shadow cast by the sudden death of Stephen Hawking! A Plus article by Marianne Freiberger does him handsomely. More nuanced is Peter Woit's response at Not Even Wrong which deals with some of the religious and philosophical fall-out inevitably attaching to Hawking's superstar status. There is more in some follow-up posts and Not Even Wrong attracts quantities of well-moderated comments. There is no-one more worth listening to than an outsider looking in and Peter Woit deliberately presents himself, I think, in this role. He and his commenters are also very insightful on March's other big news story, the Abel prize award to Robert Langlands. Back to Plus, though, for a fine popular overview by Rachel Thomas.
Not Even Wrong is named for Wolfgang Pauli's jibe. From George Box we have Wrong But Useful wherein Colin Beveridge and friends summarise their latest podcast touching on many things with Pi Day and Chalkdust issue 7 getting a mention. Any other blogs named after scientific quotes? Respond in the comments section below.
How many 'geniuses' have I mentioned so far? Pauli, Box, Conway, Hawking, Langlands (and Abel): add Georg Cantor, as represented by Rob J Low's very lucid Cantor and infinity in a countable universe. But I put 'genius' in quotes because it's a dangerous label as Thony Christie (who is to history of science as Peter Woit is to theoretical physics) reminds us in Dangerous Twaddle. His main target is the 'mathematics can send you mad' meme but the two things are related, hence the 'mad genius' cliché. On 'genius', James Propp is aware and self-aware in The Genius Box. This gets a March 8th star as well: the section Genius and Gender is a valuable introduction to the contribution of Moon Duchin.
James Propp offers some detailed analysis of primary sources and this is matched by the resourceaholic blog's look at 18th century arithmetic. Although light in tone, it's the kind of scholarship I think Thony Christie would approve of. Equally scholarly but beautifully twenty-first century to look at are Roice Nelson's animations of Isometry Classes of Hyperbolic 3-Space. Back in two dimensions, Paulo Ferro at Maths Challenges, tells us about the spirograph curve creator and links to a great simulator (I think it's by Nathan Friend, look out for the link, which is almost hidden by an amazon ad). Here's one I did:
Fun times! While on spirals, David Bachman's blog has Lesser Known Facts About Sunflowers and Pinecones (Pt. 2) (there is a link to part 1 which came out in February). It is a beautifully illustrated piece about modelling Fibonacci spiral growth in plants.
I was tempted to end with a bit of nostalgia: back in 2014 I proudly hosted my second ever Carnival of Mathematics (no. 112) and it was World Cup time and people were submitting blog posts about it. Four years on and Matthew Scroggs is blogging about calculating, via a neat bit of probablity, the likely cost of collecting World Cup stickers 2018.
But actually it seems more poetic to end with a bit of poetry, and JoAnne Growney at Poetry with Mathematics inspires me:
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