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LaTeX/TikZ to draw a star graph $K_{1,n}$

For a diagram for a class this week, I’ve written a LaTeX command to draw star graphs using TikZ. A star graph $K_{1,n}$ is a graph with a single central node, $n$ radial nodes, and $n$ edges connecting the central node to each radial node. I am sharing this here in case it is useful to anyone else.

Baking Babylonian cuneiform tablets in gingerbread

The MathsJam conference has a baking competition. My friend the archaeologist Stephen O’Brien tweeted a while ago a link to a fun blog post ‘Edible Archaeology: Gingerbread Cuneiform Tablets‘. Babylonian tablets are among the earliest written evidence of mathematics that we have, and were produced by pressing a stylus into wet clay.

So it was that I realised I could enter some Babylonian-style tablets made from gingerbread.

I made a gingerbread reconstruction of a particular tablet, YBC 7289, which Bill Casselman calls “one of the very oldest mathematical diagrams extant“. Bill writes about the notation on the tablet and explains how it shows an approximation for the square root of two. I’m sure I didn’t copy the notation well, because I am just copying marks rather than understanding what I’m writing. I also tried to copy the lines and damage to the tablet. Anyway, here is my effort:

Babylonian tablet in gingerbread

In addition, I used the rest of the dough to make some cuneiform biscuits. I tried to copy characters from Plimpton 322, a Babylonian tablet thought to contain a list of Pythagorean triples. Again, Bill Casselman has some interesting information on Plimpton 322.

Babylonian cuneiform biscuits

Below, I try to give a description of my method.

Handing over @mathshistory

On 5th October 2010, eight years ago this week, I sent a tweet from a Twitter account I had registered on behalf of the British Society for the History of Mathematics (BSHM). I was on BSHM Council at the time and, mindful of the Society’s charitable aim to develop awareness of the history of mathematics for the public benefit, I proposed starting a Twitter account. I thought a good way to generate a background level of activity for the account was to tweet a daily mathematician, taking my lead from the MacTutor website facility. So I set up @mathshistory and sent the first tweet, announcing the anniversary of the birth of Bernard Bolzano.

LaTeX for typesetting a multi-pile Nim game

I am preparing to teach our new final year module ‘Game Theory and Recreational Mathematics’. So I’m thinking about game typesetting in LaTeX (texlive-games is useful in this regard). I was looking for an easy way to display multi-pile Nim games. Usually, I find searching “latex thing” finds numerous options for typesetting “thing” in LaTeX, but here I was struggling.

Nim objects could be anything, of course, but conventionally sticks or stones are used. There are various types of dot in LaTeX that might look like stones, but somehow a line of dots didn’t seem satisfactory. There are various ways to draw a line (not least simply typing ‘|’), including some tally markers (e.g. in hhcount). My problem with these (call me picky) is that they are all identical lines, and a ‘heap’ of them just looks very organised. Really, I want a set of lines that looks like someone just threw them into heaps (though probably without crossings for the avoidance of ambiguity). So I wrote my own.

Second place in a single-elimination tournament

Trophy for Joint 2nd Place, awarded to "???"

I made a silly joke, and it made me think.

You may be aware that our own Christian Lawson-Perfect is running the Big Internet Math-Off here at the Aperiodical, a single-elimination tournament with sixteen competitors. I was knocked out in round one by the brilliant Alison Kiddle. I joked that if Alison went on to win, then I’d be joint second.

I’ve been mulling this over and I felt there was something there in thinking about the placement of the non-winners in such a tournament, so I had a play.

Are there More or Less stars than grains of beach sand?

This week’s episode of More or Less on the BBC World Service answered a question that involved estimating big numbers: Are there more stars than grains of beach sand?

This claim was famously made by Carl Sagan in the seminal programme Cosmos.

The cosmos is rich beyond measure. The number of stars in the universe is larger than all the grains of sand on all the beaches of the planet Earth.

More or Less come to a fairly standard answer, that Sagan was correct. This sort of problem, which involves approximating unknowable numbers based on a series of estimates, is called a Fermi problem. I’ve written about Fermi problems here before. The More or Less approach to answering this raised a question from a reader of this blog.

Alright, actually Paul is one of the writers of this blog, rather than a reader. Even so, are his concerns warranted?