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Exactly how bad is the 13 times table?

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Let’s recite the $13$ times table. Pay attention to the first digit of each number:

\begin{array}{l} \color{blue}13, \\ \color{blue}26, \\ \color{blue}39, \\ \color{blue}52 \end{array}

What happened to $\color{blue}4$‽

A while ago I was working through the $13$ times table for some boring reason, and I was in the kind of mood to find it really quite vexing that the first digits don’t go $1,2,3,4$. Furthermore, $400 \div 13 \approx 31$, so it takes a long time before you see a 4 at all, and that seemed really unfair.

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Approaching Fermi problems with the approximate geometric mean

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I gave a talk on Fermi problems and a method for approaching them using the approximate geometric mean at the Maths Jam gathering in 2017. This post is a write up of that talk with some extras added in from useful discussion afterwards.

Man talking on the phone

Enrico Fermi apparently had a knack for making rough estimates with very little data. Fermi problems are problems which ask for estimations for which very little data is available. Some standard Fermi problems:

  • How many piano tuners are there in New York City?
  • How many hairs are there on a bear?
  • How many miles does a person walk in a lifetime?
  • How many people in the world are talking on their mobile phones right now?

Hopefully you get the idea. These are problems for which little data is available, but for which intelligent guesses can be made. I have used problems of this type with students as an exercise in estimation and making assumptions. Inspired by a tweet from Alison Kiddle, I have set these up as a comparison of which is bigger from two unknowable things. Are there more cats in Sheffield or train carriages passing through Sheffield station every day? That sort of thing.

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Review: Closing the Gap, by Vicky Neale

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Did you read Cédric Villani’s Birth of a Theorem? Did you have the same reaction as me, that all of the mentions of the technical details were incredibly impressive, doubtless meaningful to those in the know, but ultimately unenlightening?

Writing about maths, especially deep technical maths, so that a reader can follow along with it is hard – the Venn diagram of the set of people who can write clearly and the set of people who understand the maths, two relatively small sets, has a yet smaller intersection.

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A winning competition

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As part of this year’s MathsJam gathering, as for the last few years, we held a competition competition (you may have seen Peter’s recent post about his entry to the same event in 2014). My competition was the winner, and I thought I’d share with you some of the entries, as I very much enjoyed reading them all.

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The competition I entered into the first MathsJam Competition Competition

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A couple of weekends ago was the big MathsJam gathering (I might call it a recreational maths conference, but this is discouraged). Two of the delightful sideshows, alongside an excellent series of talks, were the competitions. The Baking Competition is fairly straightforward, with prizes for “best flavour, best presentation, and best maths”:

The first will reward a well-made, delicious item; the second will reward the item which has been decorated the most beautifully and looks most like what it’s supposed to be; and the third will reward the most ingenious mathematical theming.

You can view the entries from this year on the MathsJam website.

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MathsJam talks now online

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The talk summaries and slides from last November’s MathsJam conference are now online!

MathsJam is a monthly maths night that takes place in over 30 pubs all over the world, and it’s also an annual weekend conference in November. The conference comprises 5-minute talks on all kinds of topics in and related to mathematics, particularly recreational maths, games and puzzles.

The talks archive has now been updated with the 2015 talks – there’s a short summary of what each talk was about, along with any slides, in PPT and PDF format, and relevant links.

 

 

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