Maths at the Movies: Predicting Income

In two years (so far) of pandemic responses many business in many sectors have suffered. Just one of these is the movie industry, with cinemas now trying to recoup revenue lost during long periods of closure and reduced patronage.

Hollywood Theatre (1935) Entrance by Heritage Vancouver/Patrick Gunn is licenced under CC BY-NC-ND 2.0

The article linked below, posted by the Institute of Mathematics and its Applications (IMA), briefly introduces four methods for modelling the performance of past movies at the box office with a view to predicting future income. As with most explorations of mathematical topics, the principles covered here could be applied to different situations in other industries.

Could Mathematics Be Big at the Box Office?

Want to learn more about differential equations? Try this free course from Alison.

The Man Who Knew Infinity - Maths in the Movies

The Man Who Knew Infinity (DVD):
amzn.to/3mCIljh

At the time of writing The Man Who Knew Infinity is available to watch on BBC iPlayer, or it can be bought or rented via Amazon Prime Video.

The Man Who Knew Infinity is a biographical drama about real-life Indian Mathematician Srinivasa Ramanujan, who made a number of contributions to pure mathematics during his relatively short life. The movie focuses on his work with English Mathematician G. H. Hardy at Cambridge University following a postal correspondence that convinced Hardy of Ramanujan's brilliance.

Every GCHQ Christmas Card

For the past few years (with some gaps) GCHQ have released a very special card at Christmas. Not just a device for wishing recipients the best of the season, it includes puzzles to solve! These are usually presented as a series of brainteasers of increasing difficulty, with the early stages usually pretty accessible, and the later ones a bit more challenging.

Here are links to each one so far, with a preview of each:

2021

GCHQ's 2021 Christmas Card - Preview

Links: GCHQ Blog Post | Card (.pdf) | Card adapted for schools (.pdf) | Solutions (.pdf)

The Allusionist: Num8er5

The Allusionist is a podcast focusing on language, and this episode, Num8er5, is all about, well, numbers. You can listen to it in the player below, or read more information (including a link to its page at the Allusionist) underneath that.

The episode compares the development and use of numbers as expressed verbally with numeral systems for writing them down. It provides an interesting thread through aspects of history that are relevant to both language and mathematics, and touches upon number use across different societies, cultures and civilisations throughout history. Click the link below to listen to the episode on The Allusionist's website, where there is further information and links to related resources including other episodes.

The Allusionist: Num8er5

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:

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.

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

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:

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.

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

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:

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.

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, 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

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 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

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.

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:

How do Lava Lamps Help With Internet Security?

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.

Calculating distance to the horizon from NCETM on Vimeo.

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

Calculating Distance to the Horizon

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

The Unexpected Math Behind Van Gogh's "Starry Night"

This TED-Ed Original lesson discusses the uncannily accurate representation of the mathematically difficult concept of turbulence in Van Gogh's famous painting, and its potential relationship to his state of mind.

Watch the narrated animation in the player above or click the following link to visit the TED-Ed page which includes a transcript:

The Unexpected Math Behind Van Gogh's "Stary Night"

Algebra: the Maths Working to Solve the UK’s Supply Chain Crisis

Whether its roots were in the Covid-19 pandemic, Brexit, or a mixture of both, the UK suffered supply chain problems in 2021, with supermarket shelves quickly running out of common goods including pasta, bottled water and toilet paper. This article from The Guardian discusses the role of algebra in improving the situation.

Screengrab: Algebra: the Maths Working to Solve the UK’s Supply Chain Crisis

Algebra: the Maths Working to Solve the UK’s Supply Chain Crisis

Maths is Vital

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 DNA sequencing and and the massive amounts of data analysis required.

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

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.

Maths Takes Off

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 aerodynamics.

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

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.

Maths Evens the Odds

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 probability, chance and risk.

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

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.

Maths Connects

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 graph theory and its uses explaining the connections in all sorts of networks.

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

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.

Maths Hots Up

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 unravelling the mysteries of solar storms using mathematics.

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

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.

If you're interested in astronomy and space science, why not give Blogstronomy a try (you can find out more about the Sun at this tag)?

What Would Florence Nightingale Make of Big Data?

From the BBC's "ideas" series, here's David Spiegelhalter introducing Florence Nightingale's work on statistics in a 4-minute video, and looking at how we can use the same principals to make sense of the data that is thrown at us from all angles in today's superconnected world!

Maths is Cool

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 catastrophe theory and its relevance to unstable icebergs.

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

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.

Mathematics in Work: Civil Servant

Another in Cambridge Mathematics' Interviews and Intersections series: Chris is a Customer Support Officer in Leicester, and he is interviewed here about his life and work, and where mathematics makes an appearance in both:

Intersections: Mathematics and the Civil Servant

Chaos in the Weather

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 chaotic behaviour in things like the stock market and weather.

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

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.

Maths Stirs

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 mathematics of vortices and mixing substances, as encountered in hurricanes and coffee mugs alike.

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

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.

The Bletchley Park 30 Day Challenge

Back in March 2020, just before the first Covid-19 Lockdown I was still working at Bletchley Park and with input from some of my colleagues in the Learning team devised 30 challenges which were tweeted 3 per week over the following 10 weeks. We bashed these out over the weekend, in our own time, before being furloughed but a whole load of love (and mild obsession) for all things Bletchley Park went into devising these in a short space of time.

Now we're in our third (ish) lockdown, for most of the people who worked on them their time at BP is but a distant memory, having been made redundant* some months ago. The challenges themselves have disappeared into the depths of BP's social media feeds... until now!

I've collected all 30 tweeted challenges and embedded them into one page so that you can work through them all at your leisure, or just pick and choose the ones you fancy!

Click the screenshot below to find them (but don't tell anyone! Mum's the word...**):

If you click on the timestamp at the bottom of each embedded tweet you will be taken to the original post on twitter, where you can see conversations resulting from each one, and maybe get one started again! Better still, why not respond to the original posts for the challenges you complete with a picture or other content showing off your work!

* Including me. Needless to say, neither this post nor the page to which it points are at all sanctioned or endorsed by the Bletchley Park Trust and if they'd compiled these challenges on their own website I would certainly have linked to that instead.

** No isn't. Please tell everyone! It's not secret any more...

The Alan Turing Cryptography Competition

Each year, starting towards the end of January, the maths department at the University of Manchester release their Alan Turing Cryptography Competition into the wild.

Much like the National Cipher Challenge it consists of multiple challenges of increasing difficulty that are released on a weekly basis, usually on Mondays.

Click the image/text below to visit and sign up. Come back to this page and let us know how you get on in the comments (no spoilers, though)!

Maths Counts

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 Fibonacci, the Golden Ratio, and their appearances in nature and art.

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

World Mathematical Year 2000 London Underground Posters

Also available to purchase in a set of all 12 posters pre-printed at 61cm x 28cm from the Mathematical Association.