A branch of mathematics, known as non-Euclidean geometry, is helping to bring beloved films to life on the big screen.
With the Golden Globes kicking off this year’s movie awards season today, Australian Mathematical Sciences Institute (AMSI) Summer School 2016 speaker, Margaret Wertheim, believes the real winner of best-animated feature film may be mathematics.
“Animated films have helped to bring about a revitalisation of geometry in a beautiful relationship between an ancient branch of mathematics and modern entertainment,” she says.
It is a relationship that the internationally respected science communicator will explore as she tells the story of hyperbolic geometry at the AMSI Summer School 2016 public lecture, Corals, Carbon and the Cosmos: The Story of Hyperbolic Space this month.
The computer-generated imagery (CGI) industry behind 2016 Golden Globe nominees The Good Dinosaur, Inside Out, and The Peanuts Movie is a significant employer of geometry PhDs.
“Films such as Avatar and Shrek have pioneered the use of geometric modelling to create ever-more intricate and wondrously believable animated worlds,” says Ms Wertheim.
Animation is created using a series of dots, line segments and triangles. Making light work of difficult imagery, the use of triangles allows animators to bring the swish of a dress or the flick of a tablecloth to life. This requires software packages that model non-Euclidean surfaces and forms, including hyperbolic structures.
“Geometry expertise is needed to address the essentially mathematical challenge of giving surfaces such as fabric and skin naturalist forms in three-dimensional space,” she explains.
Hyperbolic structures, a particular kind of non-Euclidean form are not confined to animated film. They exist in real life too, with natural examples surrounding us on land and in our oceans.
“Cacti, sea sponges and many varieties of coral found in the Great Barrier Reef are all hyperbolic structures. This increases their surface area enabling them to feed and thrive. As a sea creature, if you are rooted to the spot and can’t go chasing down your lunch, a hyperbolic surface maximises your potential to catch it on the fly,” she says.
Margaret has attracted worldwide attention as co-creator of one of the world’s largest participatory mathematics projects, a crochet model of the Great Barrier Reef. Thanks to an exhibition tour and book release the project has had a profound and unexpected impact.
“As well as nature’s love affair with hyperbolic structures, this project allowed us to highlight the impact of climate change and CO2 on Australia’s greatest natural wonder,” she says.
AMSI Summer School is Australia’s leading residential mathematical sciences training event. The four-week program provides advanced courses, networking and career development opportunities to give students a leading edge as they establish their research careers.
“International speakers such as Margaret Wertheim provide a chance for the public to see mathematical theory as it applies in the real world,” says AMSI Director Professor Prince.
Margaret Wertheim will deliver this year’s AMSI Summer School public event from 6 pm – 7.30 pm on 14 January at the Swanston Academic Building, RMIT University, 445 Swanston Street. For more information and bookings, visit http://ss16.amsi.org.au.
The Department of Education and Training and the Australian Mathematical Sciences Institute jointly fund AMSI Summer School with support from RMIT University, the Australian Mathematical Society, the Australia New Zealand Industrial and Applied Mathematics Society and 2016 event sponsors Optiver and City West Water.
Professor Geoff Prince, AMSI Director
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