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Square wheels in an Italian maths exam

There have been various stories in the Italian press and discussion on a Physics teaching mailing list I’m accidentally on about a question in the maths exam for science high schools in Italy last week.

The paper appears to be online.

(Ed. – Here’s a copy of the first part of this four-part question, reproduced for the purposes of criticism and comment)

The question asks students to confirm that a given formula is the shape of the surface needed for a comfortable ride on a bike with square wheels. (Asking what the formula was with no hints would clearly have been harder.) It then asks what shape of polygon would work on another given surface.

What do people think? Would this be a surprising question at A-level in the UK or in the final year of high school in the US or elsewhere? Of course, I don’t know how similar this question might be to anything in the syllabus in licei scientifici.

The following links give a flavour of the reaction to the question:

6 hours, 1 question out of 2 in section 1, 5 out of 10 in section 2. My own initial reaction is that if I had to do this exam right now I’d do question 2 in section 1 but I’ve not actually attempted question 1 yet.

Alexandre Grothendieck’s notes archive to be released online

News from France, where the family of the late Alexandre Grothendieck, legend of basically all maths, have finally reached an agreement with the academic community about his huge archive of written notes. Discussions have been ongoing for a while but it’s finally been agreed that the notes can be released online for the community at large to take advantage of.

The notes comprise over 100,000 pages of mathematics, diagrams and letters to collaborators, and an initial chunk of over 18,000 pages will be online from 10th May on the University of Montpellier’s website. It’s expected that many undiscovered mathematical treasures might be found within, although the challenge of reading through and deciphering it all may take a Polymath-style mass effort.

More information

The notes of the mathematician Alexandre Grothendieck arrive on the net, at Libération (in French)

via Jordan Ellenberg on Twitter

Dani’s OEIS adventures: triangular square numbers

Hi! I’m Dani Poveda. This is my first post here on The Aperiodical. I’m from Spain, and I’m not a mathematician (I’d love to be one, though). I’m currently studying a Spanish equivalent to HNC in Computer Networking. I’d like to share with you some of my inquiries about some numbers. In this case, about triangular square numbers.

I’ll start at the beginning.

I’ve always loved maths, but I wasn’t aware of the number of YouTube maths channels there were. During the months of February and March 2016, I started following some of them (Brady Haran’s Numberphile, James Grime and Matt Parker among others). On July 13th, Matt published the shortest maths video he has ever made:

Maybe it’s a short video, but it got me truly mired in those numbers, as I’ve loved them since I read The Number Devil when I was 8. I only needed some pens, some paper, my calculator (Casio fx-570ES) and if I needed extra help, my laptop to write some code. And I had that quite near me, as I had just got home from tutoring high school students in maths.

I’ll start explaining now how I focused on this puzzle trying to figure out a solution.

Pale imitations: newcomers in the Math/Maths Podcast hiatus

Since the start of the year, the Math/Maths Podcast has been on hiatus. I’m very much enjoying the extra thesis-writing time but apparently this has left some missing their regular mathematical listen. Not infrequently I get an email from someone wishing me well with my thesis and asking when we’ll be back podcasting. Well, nature abhors a vacuum and here are three offerings that I’m aware are working to fill the void. (Oh, and “pale imitations” – I’m joking, of course!)

All Squared (RSS, iTunes)

My Aperiodical co-conspirators Katie Steckles and Christian Perfect started All Squared, a maths magazine podcast, in February. The description for the first episode (or “number”, as Katie and Christian have it) overtly points out the “unusual paucity of maths podcasts at the moment” and promises “a half-hour podcast featuring maths, guests, puzzles and links from the internet”. The name is designed to be recognisable to mathematicians, who might find themselves reporting that an expression is “all squared”. As someone who named a podcast as overtly as it is possible to be, “Math/Maths”, this obfuscation amuses me. The three episodes so far have been enjoyable with a guest and main topic in each. As far as I’m concerned, this is far more the Aperiodical podcast that should exist than is The Aperiodcast with that third guy.

TES Maths Podcast (iTunes)

This one started just before Samuel Hansen and I went on our hiatus, but if you enjoyed the teaching aspects of what we did you can get a lot more on the theme from Craig Barton and his guests on the TES Maths Podcast. Craig promises “to share the latest news, resources and ideas that are relevant to secondary/high-school maths teachers and general number enthusiasts”.

Wrong, but Useful (RSS)

Wrong, but Useful is a new podcast featuring “a mathematical conversation” between Colin Beveridge and Dave Gale that sets out its stall as a response to the lack of Math/Maths episodes. The title is another nod to the mathematically minded without being overt, referring to a quote from George Box and Norman Draper who wrote “essentially, all models are wrong, but some are useful” (Empirical Model-Building and Response Surfaces, 1987). Episode 1 sees Colin and Dave finding their feet in a rambling, wide-ranging mathematically-themed discussion. There were a couple of awkward moments that gave me Math/Maths early episode flashbacks but I’m looking forward to Colin and Dave getting into the swing for the next episode.

Happy listening!

Podcasting update

I have a job. This is not the podcasting update, but it does affect it! If you have listened to the latest Math/Maths Podcast you will know that I will be lecturing mathematics from January while trying to finish my PhD thesis, and that we will be putting that podcast on hiatus while I do so. This means no more talking to Samuel Hansen for at least six months.

There is something you can do to fill this mathematical podcasting gap, however. Samuel is trying to raise money through a Kickstarter to allow him upgrade his equipment and improve the quality, to pay for the travel to conduct face-to-face interviews and to make this his full-time job so he can concentrate on a regular release schedule, for his work in maths (math) and science communication over at ACMEScience.com.

At Kickstarter, Samuel says:

ACMEScience.com has spent the last four years trying to do something that very few others have ever attempted, create entertaining, insightful, and interesting content about mathematics and science. Started by Samuel Hansen in the beginning of 2009, ACMEScience has produced a pop-culture joke filled mathematical panel show, Combinations and Permutations, a show that interviews everyone from the CEO of a stats driven dating site to a stand up mathematician to Neil deGrasse Tyson, Strongly Connected Components, a show that tells the stories of the fights that behind DNA, dinosaurs, and the shape of the universe, Science Sparring Society, a video interview show that has featured predatory bacteria and crowdsourced questions, ACMEScience News Now, and a series of hour long journeys into the world of competitive AI checkers computers and stories of the most interesting 20th C mathematician and much more, Relatively Prime.

You may remember that Samuel raised money through a Kickstarter before, for the extremely well-received documentary series Relatively Prime. So you might judge this as evidence that he is capable of delivering this project. However, you may also remember that if he doesn’t raise the whole amount he needs then he gets nothing.

There are various pledge levels, with various rewards. Some of these are aimed at the individual who wants to own a piece of the project. Others are aimed at people who want to sponsor/advertise via the shows and get their message out there. Looking at the level of pledges so far, Samuel could really do with a few companies or individuals who want to get a message out to a mathematics or science audience coming forward and pledging some money. Relatively Prime was very well listened to, and you could get your message to a large, focused, engaged set of listeners.

There is not long to go (only four days at time of writing) and it doesn’t look good. So please pitch in and also tell everyone you know via your own blog/podcast/social networks/etc. so that others will support his effort.

Here is the video in which Samuel makes his case. It’s six minutes so at least watch that! The Kickstarter page is ACMEScience.com by Samuel Hansen. Donating is easy through Amazon payments.

Martin Gardner celebration week in Nottingham

Last Sunday saw the anniversary of the birth of Martin Gardner, and as a celebration, the Gathering for Gardner people planned a world-wide party ‘G4G Celebration of Mind‘. It happened to be Maths Jam night on Tuesday, so we put the Nottingham Maths Jam on the G4G-COM map. Then on Friday three of us had agreed to take a puzzles stall to the Nottingham STEM Pop Up Shop, so I added this to the map as well.

A Celebration of Mind party is supposed to “celebrate the legacy of Martin Gardner on or around Sunday, October 21, 2012 through the enjoyment of [one or more of] Puzzles, Magic, Recreational Math, Lewis Carroll, Skepticism and Rationality”.

At Maths Jam I printed a bunch of flexagon material from the Flexagon Party page. I also had a plan: having finished two jobs in recent years with piles of business cards outstanding, I brought these to try some business card origami. In fact, we decided to make a business card Menger sponge. So we started folding.

Business card folding begins

Meanwhile, John Read had come equipped with some colourful designs to make hexahexaflexagons.

John Read’s first hexahexaflexagon of the evening. Designs from flexagon.net.

John Read’s second hexahexaflexagon. Designs from flexagon.net.

At the same time, Jon made a trihexagon.

Trying to make a triflexagon

Finally, after much business card folding,we had a Menger sponge* (*not a real one, it being a fractal after all!). Here it is, in Maths Jam-style, balanced on a pint of beer.

The completed business card Menger sponge

And here’s a shot through the Menger sponge, where a geometry puzzle is being attempted.

Through the completed business card Menger sponge, some geometry is happening

Here are a couple of the other puzzles that we tried, some from the #MathsJam tag on Twitter:

You have 100 coins, 10 of which are showing heads and 90 of which are showing tails (though these are indistinguishable by touch). Blindfolded, you must divide the coins into an even number of heads and tails. 

Which is bigger, 3^(21!) or 2^(31!)?

Then on Friday we made our way to Broadmarsh shopping centre for our afternoon at Nottingham’s STEM Pop Up Shop.

Nottingham STEM Pop Up Shop welcome notice

Here’s a picture of our stall, with Kathryn Taylor presiding, and in the foreground the posters about Martin Gardner, mathematical games and mathematicians that I had printed. Someone did ask me who Martin was and I explained a little; I think I also convinced him to come to Robin Wilson’s talk on Lewis Carroll next month in Derby.

Martin Gardner posters on our stall

Here’s the detail of our stall, which we called ‘Solving it like a mathematician’. You can get details of the set of puzzles on my website.

The STEM Pop Up Shop ‘Solving it like a mathematician’ stall

Looking around the shop, I requisitioned the Alan Turing postcards from the ‘My Favourite Scientist’ set for our stall!

Alan Turing postcards

Here’s a wider view of the stall, with Kathryn entertaining a customer.

Kathryn Taylor at our stall

And finally, here’s John Read bewitching a crowd with the loop on a chain trick.

John Read enthuses a crowd with a ring on a chain

Thank you for reading!

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Nobel week – a place for mathematics?

In a blog post last week, Alex Bellos said:

It is often said that the reason Alfred Nobel did not endow one of his prizes in mathematics was because his wife was having an affair with a mathematician.
While this story has been debunked it is nevertheless frustrating to mathematicians, especially during Nobel week, that the noblest of the sciences is ignored by the Royal Swedish Academy of Sciences.

As an alternative, Alex offers the Mental Calculation World Cup.

A while ago, I wrote a flippant little piece in which I claimed that “Most of the Nobel Prizes are for Mathematics“. While perfectly valid and interesting mathematics takes place within mathematics itself, it is an interesting aspect of mathematics that its applications take place on the boundaries with, or even within, other disciplines. This creates some issues for those championing mathematics. Some people would like to assess the economic impact of mathematics but this is a difficult task. At what point does an application of mathematics belong to science, engineering or technology?

The point of the IMA Mathematics Matters series of articles, as I understand it, is to show where modern mathematics research has had its impact, even though that impact may be “perfectly hidden in its physical manifestation”. Some people would take the result of a piece of research to be “not mathematics” as soon as it finds an application. Unfortunately, defining a piece of work as ‘not mathematics’ as soon as it is applied is a way to ensure that all measures of economic value of the impact of mathematics are zero; yet it is clearly the case that much of science, engineering and technology would be naught without the mathematics that underpins it.

This is a balance we try to strike when finding stories for the Math/Maths Podcast; many interesting stories, and certainly those more likely to be written up by university press offices or the media, are those which apply mathematics in some other area. How far do we follow a story before declaring it “not mathematics” and turning our attention elsewhere?

It is with this mindset that I view the Nobel Prizes. Much of the work for which the prizes are awarded is underpinned by mathematics. I see ‘Nobel week’ as an opportunity for mathematicians to go in search of the mathematics behind each prize, rather than to retreat and complain about the lack of a prize specifically for mathematics.