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2021/12/01

Maths is Forever

One of a collection of posters produced for World Year of Mathematics 2000 and displayed on trains in the London Underground, this one focuses on the Twelve Days of Christmas, with a quick nod to proof.

This is a low-res version. Download the full-sized image at the link below:

2021/11/17

Mathematical Objects: Enigma Machine

Shortly before leaving Bletchley Park I guested on the Aperiodical's Mathematical Objects podcast talking about Enigma machines. Listen to this episode in the player below:

In the episode I join Katie Steckles and Peter Rowlett for an informal conversation about the famous yet widely misunderstood Enigma machine and some of the mathematics that surrounds this legendary device.

Click the link below to visit the podcast episode's page over at the Aperiodical:

Mathematical Objects: Enigma Machine

2021/11/01

Maths Makes Waves

One of a collection of posters produced for World Year of Mathematics 2000 and displayed on trains in the London Underground, this one focuses on waves and wave propagation.

This is a low-res version. Download the full-sized image at the link below:

2021/10/30

Differential Equations and Speed

The post linked below the image, from Plus Magazine's Maths in a Minute series, briefly introduces the idea of differentiation and differential equations.

It makes an implicit link between prior knowledge of the relationship between speed, distance and time, and the more abstract notion of differential equations which is usually encountered by students later in their maths learning journey. The article also includes some links to further examples of differential equations and their use in real-world problem solving.

Maths in a Minute: Differential Equations

2021/10/01

Maths Breaks the Code

One of a collection of posters produced for World Year of Mathematics 2000 and displayed on trains in the London Underground, this one focuses on codes, ciphers and secret communication.

This is a low-res version. Download the full-sized image at the link below:

2021/09/24

Maths Explains Bird Behaviour

This article from the Yorkshire Post in 2020 introduces us to Natasha Ellison, a former maths teacher who returned to university to complete a PhD, for which she studied some odd behaviour of long-tailed tits, birds native to Sheffield.

A long-tailed tit perches on a branch looking towards the camera.
A Long-Tailed Tit, by Tim Felce (Airwolfhound), CC BY-SA 2.0, via Wikimedia Commons

These birds split up into groups around the local landscape, which is not something that non-territorial birds tend to do. Ellison and her team used mathematical modelling to try to understand it, developing techniques that could potentially applied to further studies of other parts of the animal kingdom. A research article authored by Ellison and other members of her team is available at the Journal of Animal Ecology (Open Access), and you can read the Yorkshire Post's article at the link below:

How Maths is Unlocking Nature's Secrets in Sheffield's Rivelin Valley

2021/09/22

Sourdough Hydration

My social media feeds during the Covid-19 Pandemic lockdowns were awash with furloughed friends indulging in hobbies and pastimes, new and old. A lot of these involved some sort of cooking and baking, with two things coming out on top: banana bread and sourdough.

A jar of bubbly sourdough starter viewed from above
A jar of sourdough starter

Sourdough bread is made from fermented (which is why it's sour) dough. The fermentation process takes time, so sourdough makers traditionally use a "starter", which is a fermented mixture of flour and water. A portion of this is taken away (and mixed with other ingredients) when a new loaf is needed, with the rest of the starter forming a standby culture which is regularly "refreshed" with further additions of flour and water.

Different bakers work with different ratios of flour and water comprising their starter and refreshments. This ratio is known in the sourdough trade as "hydration" and is expressed as a percentage calculated by dividing the mass of water by the mass of flour that it is mixed with (and then multiplying by 100).

Different recipes call for different hydrations again, and these can be achieved by altering the relative amounts of flour and water in your dough. This would be easy if everyone started with the same hydration: everyone would need to add the same quantities of flour and water to achieve the same result.

Recipes on the Du's Doughs blog all assume starting from an 80% hydration starter, but blogger Erica has written a post to help those who start with other hydration values to obtain the perfect consistency for each recipe too. Read the post at the link below:

Sourdough Hydration Math

2021/09/20

Lava Lamps and Internet Security

The security of data in our internet-connected world hinges on the generation of very large random numbers. True randomness, however, is next to impossible to achieve, so modern internet security firms work very hard to find ways to generate numbers that seem as random as possible. One such company has found a solution in the form of lava lamps.
A lava lamp is a bottle filled with water and blobs of wax, both brightly coloured. A hot lamp in the base of the lamp heats up the contents of the bottle, melting the wax which gloopily rises, where it cools and falls back to the base before being heated up and rising again. The motion of the wax in the lamp is chaotic, which means that it is very hard to predict.

A row of brightly coloured lava lamps.
Lava Lamps, by Mike Mozart

Internet security company Cloudflare have in their headquarters not just one lava lamp, but one hundred of them. There is a camera constantly watching this wall of chaotic-motion generators. As digital images are stored as a series of numbers describing aspects of each pixel, and each pixel's input is based on a highly chaotic process, this means that each resulting image file does a very good impression of a random number.
Read more about this on Cloudflare's website at the link below:

2021/09/19

Calculating Distance to the Horizon

Navigation Officer Thomas McAuley demonstrates how to calculate the visible distance to the horizon using circle theorems and Pythagoras' theorem.


Watch the video in the player above or click the following link to watch at NCETM's Vimeo account:

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