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The Actual Maths
_Real_ reallife maths.
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2021/12/01
Maths is Forever
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
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 realworld problem solving.
Maths in a Minute: Differential Equations
2021/10/01
Maths Breaks the Code
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 longtailed tits, birds native to Sheffield.
A LongTailed Tit, by Tim Felce (Airwolfhound), CC BYSA 2.0, via Wikimedia Commons 
These birds split up into groups around the local landscape, which is not something that nonterritorial 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 Covid19 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 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
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 chaoticmotion 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.
2021/09/19
Calculating Distance to the Horizon
2021/09/18
Mathematics in Work: Shop Floor Assistant
In this Cambridge Mathematics' Interviews and Intersections post, Shop Floor Assistant Neale discusses is feelings about and the place of mathematics in his work:
Intersections: Mathematics and the Shop Floor Assistant
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