A brilliant ‘geometric ballet’ of sound, shape and symmetry on the theme of 180°

Over the last decade or so, the inherent beauty and elegance of maths has proven fertile territory for video artists looking to put their keen eyes, exacting minds and technical wizardry on display. But as the old proverb goes and this 1966 short film shows, there is nothing new under the sun. A classic production from the National Film Board of Canada, this short animated film sets some 300 transformations, divisions and subdivisions of triangles to a piano waltz, making for a viewing experience that still enchants 50 years later.

Embarrassment is love when you’re hanging with your pre-adolescent kid brother

The Toronto-based filmmaker Dominique van Olm and her younger brother Dexter are separated by 13 years and hundreds of miles, so they spend very little time together. In Little Brother – a ‘hybrid of documentary and narrative fiction’ – van Olm takes that reality and turns it into an experiment in directing and bonding. For the project, Dexter flew to Toronto for the first time, and spent four days with his sister. Trailed by a barebones film crew, van Olm dutifully dragged Dexter to places she thought a 12-year-old boy might enjoy – including a pizzeria, an aquarium and a roller rink. The resulting short film, composed of brief, unscripted vignettes from their time together, is an accomplished and refreshingly restrained work. With a constant undercurrent of slight discomfort, subtle humour and very unspoken familial love, it traces the distinctive contours of this particular sibling relationship and the more universal afflictions of adolescence – inscrutable moods, halting communication and a perpetual state of embarrassment while in the company of family.

Where Soviet cars go to not quite die – driving adventures in northern Russia

The Lada is a stalwart symbol of Soviet Russia. It has also been considered one of the worst cars ever made. Its heyday, if it had one, was in the 1970s, but a substantial number of vehicles remain on the roads today, and hold a special place in the hearts and minds of many Russians. To tell the story of this much-ridiculed car, the filmmaker Dieter Deswarte, the cinematographer Annegret Sachse and the sound engineer Yulia Glukhova travelled the Russian north, from Murmansk to Siberia, to find where the cheap and easily repairable – if reliably unreliable – vehicles are still in action. Along the way, they got to know a colourful range of drivers who recount the complexities of Lada ownership, and, more important still, show the car on the road – or sometimes what it takes to get it on the road. Undercutting broad Western stereotypes of a certain Russian dourness, the filmmakers find humour, warmth and kindness in their driving adventures across the icy landscape.

Lada debuted in 2014 as part of the award-winning omnibus documentary Cinetrain: Russian Winter. An ambitious and inventive filmmaking initiative, the Cinetrain project sent 21 filmmakers from around the world to all corners of Russia to explore its culture through the spectrum of stereotypes – from mail-order brides to heavy drinking. The project was inspired by the work of the influential Soviet Russian filmmaker Aleksandr Medvedkin (1900-89) who, in 1934, built a mobile film studio inside a train before setting out to document life across the country.

The Bing Bang, reincarnation and other theories of life from budding philosophers

What’s the point of life? Kindness? Recycling? Leaving your body to science? This hybrid of animation and live-action from 2009 generates good fun and plenty of food for thought from its simple premise: asking children some of the most enduring questions in philosophy. While many of the answers – including an innovative ‘exploding monkey theory’ of Homo sapiens origins –  are simply great material for the accompanying animations, others brush up against the current limits of human understanding, prompting meaningful reflection on how we think about life. With its abundance of laugh-out-loud and heartfelt moments, the Montreal-based director Karina Garcia Casanova’s playful film is a worthy tribute to the deeply creative thinking of kids.

A Nobel laureate and a flea circus join forces for an unforgettable demonstration of inertia

The Physical Science Study Committee (PSSC) was formed in 1956 at the Massachusetts Institute of Technology with the mission to create science-education materials for US high-school classrooms. Extracted from a PSSC film from 1959, the first half of this short video finds the Nobel Prize-winning physicist E M Purcell from Harvard University detailing the basics of inertia with some help from a frictionless dry-ice puck – which, by his exceptionally impassive account, is a thing that’s ‘fun to play with’. The video gets a good deal stranger in the second half, which takes viewers on a field trip to Hubert’s Museum in New York City: a long-since defunct cabinet of 10-cent curiosities that was once a Times Square mainstay. There, Hubert’s famed in-house flea circus puts its considerable talents on display as the ringmaster leads a one-of-a-kind inertia demonstration. It all makes for an impressive proof of concept, and some delightfully dated fun.