A conversation about mathematics inspired by an old textbook, Mathematics in Theory and Practice, edited by Warwick Sawyer. Presented by Katie Steckles and Peter Rowlett.
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A conversation about mathematics inspired by a scone. Presented by Katie Steckles and Peter Rowlett, with special guest Sophie Maclean.
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I was interviewed by Nira Chamberlain, President of the Mathematical Association. I am the twelfth person to whom he has asked his question “what is the point of mathematics?” Hoping to offer something a little different, I spoke about teaching students the role mathematical modelling can play in sustainability.
Martin Gardner’s long-running column in Scientific American made it onto the front cover of the magazine twelve times. Gathering 4 Gardner refers to these cover stories as “A Gardner’s Dozen“, while pointing out that these aren’t his ‘greatest hits’ and the magazine artists didn’t necessarily reproduce the graphics as he would have liked them.
Nevertheless, I thought it would be a fun challenge to try to reproduce these in TikZ, a drawing package for LaTeX. I like TikZ, and appreciate a chance to practice my skills. Readers of the future will be able to judge how many of the dozen I produced, and how regularly I did these.
The first I chose is the cover from November 1969. Last summer I had the pleasure of visiting Scarthin Books in Cromford, Derbyshire while walking along the Derwent with my son. Inside I found a small pile of old copies of Scientific American and thought it would be nice to own a copy with an original Martin Gardner article. Naturally, I chose the issue they had where his article provided the cover image.
A conversation about mathematics inspired by the Joukowsky aerofoil. Presented by Katie Steckles and Peter Rowlett.
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My son and I visited The Mathematikum in Giessen. This is well worth a visit, we did it as a day trip by train from holiday in Frankfurt, which worked well because the museum is close to the railway station. The Mathematikum specialises in ‘hands on, minds on’ interactive activities, and we spent about 5 hours exploring the four floors. I enjoyed the open-access article The Mathematikum in Giessen by Martin Buhmann, who was kind enough to meet us and show us around.
There are some Mathematikum-made exhibits at MathsCity Leeds. I took some pictures of exhibits we had enjoyed that aren’t (to the best of my memory) available in Leeds. Here they are, in no particular order.
In the 1901 paper that named the game Nim and provided its mathematical analysis, Charles Bouton defined “safe combinations”, positions that if you leave the game in this state, your opponent cannot win. In combinatorial game theory, these are \(\mathcal{P}\) positions (the previous player has already won), as opposed to \(\mathcal{N}\) positions (the next player can win).
Bouton gives a list of “the 35 safe combinations all of whose piles are less than 16”, working in three-heap Nim. Naturally it seemed sensible to check these, so I wrote a bit of Python code to do this. Bouton’s list is good. I realised I could easily adapt my code to find out how many \(\mathcal{P}\) positions there are for three-heap Nim games with other maximum heap sizes: 1, 2, 3, and so on.
And, having generated a sequence of integers, I naturally looked to see if it was in the OEIS. This is sometimes a good way to discover that your sequence of numbers is also found in some unexpected places. It wasn’t there! So I submitted it, and I just got the exciting email “N. J. A. Sloane published your changes”. So I present A363166: “Bouton numbers: a(n) is the number of P positions in games of Nim with three nonzero heaps each containing at most n sticks”.
This is my first OEIS submission, so it’s all very pleasing, even if I’m submitting a ‘new’ sequence inspired by a 1901 paper!