A conversation about mathematics inspired by an area the size of Wales. Presented by Katie Steckles and Peter Rowlett.
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Mathematical Objects: An area the size of Wales
You're reading: Posts By Peter Rowlett
- Philippa Bonay, Director, Operations, Office for National Statistics. Appointed OBE for Public and Charitable Services.
- Anne Davis, Professor of Mathematical Physics, University of Cambridge. Appointed OBE for services to Higher Education and to Scientific Research.
- Paul Fannon, Fellow, Christ’s College, Cambridge, and Volunteer, United Kingdom Mathematics Trust. Appointed OBE for services to Education.
- Ian Hall, Professor of Mathematical Epidemiology and Statistics, University of Manchester and Senior Principal Modeller, UK Health Security Agency. Appointed OBE for services to Public Health, to Epidemiology and to Adult Social Care, particularly during Covid-19.
- David Marshall, Lately Director of Census, Northern Ireland Statistics and Research Agency (now Northern Ireland chief electoral officer). Appointed OBE for services to Official Statistics and Census-taking in Northern Ireland.
- Bruno Reddy, Founder and Chief Executive Officer, Maths Circle, Ampthill, Bedfordshire, and creator of Times Tables Rock Stars. Appointed OBE for services to Education.
- Sam Rose, Deputy Director, Data and Analysis Division, Department for Transport. Appointed OBE for services to Advanced Analytics
- Matthew Woollard, Professor of Data Policy and Governance, UK Data Archive, University of Essex. Appointed OBE for services to Data Science
- George McMath, Lately Deputy Principal, Northern Ireland Statistics and Research Agency, Northern Ireland Civil Service. Appointed MBE for services to the Northern Ireland Census.
Mathematical Objects: A ballot with Sam Hansen
A conversation about election mathematics inspired by a ballot. Presented by Katie Steckles and Peter Rowlett, with special guest Sam Hansen.
For more from Sam and the Carry the Two podcast check out this episode about Mathematics and Voting.
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Mathematical Objects: Space-filling curves
A conversation about mathematics inspired by a space-filling curve. Presented by Katie Steckles and Peter Rowlett.
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Mathematical Objects: Low bridge sign with Adam Townsend
A conversation about mathematics inspired by a low bridge sign. Presented by Katie Steckles and Peter Rowlett, with special guest Adam Townsend.
The plot discussed around 11 minutes and various other photos are available on Adam’s Height Hunt website (spoilers for the episode’s twists and turns!).
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Matrix multiplication doesn’t work like that
Earlier this week I posted a matrix multiplication worksheet on Mastodon.
If you do some of these, you might spot what’s funny about them. For example.
\[ \Large \begin{bmatrix}
\color{navy}{4} & \color{navy}{8}\\
\color{navy}{2} & \color{navy}{3}
\end{bmatrix} \begin{bmatrix}
\underline{\color{blue}{8}} & \underline{\color{blue}{8}}\\
\underline{\color{blue}{2}} & \underline{\color{blue}{7}}
\end{bmatrix} = \begin{bmatrix}
\color{navy}{4}\underline{\color{blue}{8}} & \color{navy}{8}\underline{\color{blue}{8}}\\
\color{navy}{2}\underline{\color{blue}{2}} & \color{navy}{3}\underline{\color{blue}{7}}
\end{bmatrix} \]
That is, the answer to each question can be made by treating the element in the first matrix as the first digit and the corresponding element in the second matrix as the second digit in the answer element. This is not how matrix multiplication works, and ought to be funny if I hadn’t totally over-explained the joke!
I saw one of these in a meme that Katie posted in the Finite Group chat and it got me thinking about how these work.
If we set up the matrices like this
\[ \begin{bmatrix}
a & b\\
c & d
\end{bmatrix} \begin{bmatrix}
e & f\\
g & h
\end{bmatrix} = \begin{bmatrix}
10a+e & 10b+f\\
10c+g & 10d+h
\end{bmatrix} \]
Then we establish four equations with eight unknowns.
\[ \begin{align*}
ae + bg &= 10a+e\\
af+bh &= 10b+f\\
ce+dg &= 10c+g\\
cf+dh &= 10d+h
\end{align*}\]
Since there are more unknowns than equations, these don’t have a single solution. What I wanted was to find integer solutions with all values single-digits. I wrote some Python code to find these. I removed some that look overly symmetrical – either the rows of the matrix are identical, or the same matrix is repeated. This left 73 items.
From these 73 items, I wrote a second Python script that picks 20 of them at random and builds these into a LaTeX worksheet. For the Mastodon post I reformatted this into the shape and size that I thought would display better on social media, and added in one of the squared matrices for an extra hint something weird is up, hoping people might notice this isn’t just a boring post about matrix multiplication practice!
You can view these scripts and associated files on GitHub.
4. Prime-number Pattern
I’m slowly working to (sort of) recreate Martin Gardner’s cover images from Scientific American, the so-called Gardner’s Dozen.
This time it’s the turn of the March 1964 issue. In the article ‘The remarkable lore of the prime numbers’, later included as chapter 9 in Martin Gardner’s Sixth Book of Mathematical Games from Scientific American, Gardner describes how Stanislaw Ulam in a boring meeting doodled a grid of numbers, spiralling out, then circled the primes. “To his surprise the primes seemed to have an uncanny tendency to crowd into straight lines.” These Ulam sprials, discovered the year before, contain lines related to prime-generating functions, which I have written about recently.
Particularly mathematical Birthday Honours 2024
The UK Government have announced the new set of King’s Birthday Honours. Here’s our selection of particularly mathematical entries for this year. If you spot any more, let us know in the comments and we’ll add to the list.
Get the full list from gov.uk. Spot anyone we’ve missed? Let us know in the comments.