It is high summer in the Polar Regions, and the sun never sets. Vast hordes of summer visitors cram a lifetime of drama into one long, magical day; they must feed, fight and rear their young in this brief window of plenty. Summer is a tough time for the polar bear family, as their ice world melts away and the cubs take their first swimming lesson. Some bears save energy by dozing on icy sun beds, while others go egg-collecting in an Arctic tern colony, braving bombardment by sharp beaks. There are even bigger battles on the tundra; a herd of musk oxen gallop to the rescue as a calf is caught in a life and death struggle with a pair of Arctic wolves. But summer also brings surprises, as a huge colony of 400,000 king penguins cope with an unlikely problem - heat. The adults go surfing, while the woolly-coated chicks take a cooling mud bath. Nearby, a bull fur seal is prepared to fight to the death with a rival. Fur flies as the little pups struggle desperately to keep out of the way of the duelling giants. Further south, a minke whale is hunted amongst the ice floes by a family of killer whales. The dramatic chase lasts over 2 hours and has never been filmed before. The killers harry the minke whale, taking it in turns to wear it down. Eventually it succumbs to the relentless battering. Finally, comical adelie penguins waddle back to their half a million strong colony like clockwork toys. The fluffy chicks need constant feeding and protection as piratical skuas patrol the skies. When an unguarded chick is snatched, a dramatic "dogfight" ensues.

This four-part British television series outlines aspects of the history of mathematics. Written and presented by University of Oxford professor Marcus du Sautoy, it is a co-production between the Open University and the BBC. In the first episode, Marcus du Sautoy in Egypt uncovers use of a decimal system based on ten fingers of the hand and discovers that the way we tell the time is based on the Babylonian Base 60 number system. In Greece, he looks at the contributions of some of the giants of mathematics including Plato, Archimedes and Pythagoras, who is credited with beginning the transformation of mathematics from a counting tool into the analytical subject of today. A controversial figure, Pythagoras’ teachings were considered suspect and his followers seen as social outcasts and a little be strange and not in the norm. There is a legend going around that one of his followers, Hippasus, was drowned when he announced his discovery of irrational numbers. As well as his work on the properties of right angled triangles, Pythagoras developed another important theory after observing musical instruments. He discovered that the intervals between harmonious musical notes are always in whole number intervals.

Since the birth of their trademark toy in 1958, The LEGO Group has produced over 400 billion bricks. But more and more, LEGO bricks aren't just for kids, and some take them very seriously. Adult Fans of LEGO around the globe are unashamedly declaring their love of the brick, brick artists are creating stunning and surprising creations, and LEGO master builders are building human scale and larger structures. LEGO bricks are being used educationally, therapeutically, and have provided a universal system for human creativity and our innate desire "to build." This documentary playfully delves into the extraordinary impact of the LEGO brick, its massive global fan base, and the innovative uses for it that has sprung up around the world.

Marcus du Sautoy uncovers the patterns that explain the shape of the world around us. Starting at the hexagonal columns of Northern Ireland's Giant's Causeway, he discovers the code underpinning the extraordinary order found in nature - from rock formations to honeycomb and from salt crystals to soap bubbles. Marcus also reveals the mysterious code that governs the apparent randomness of mountains, clouds and trees and explores how this not only could be the key to Jackson Pollock's success, but has also helped breathe life into hugely successful movie animations.

Without us noticing, modern life has been taken over. Algorithms run everything from search engines on the internet to satnavs and credit card data security - they even help us travel the world, find love and save lives. Professor Marcus du Sautoy demystifies the hidden world of algorithms. By showing us some of the algorithms most essential to our lives, he reveals where these 2,000-year-old problem solvers came from, how they work, what they have achieved and how they are now so advanced they can even programme themselves.

When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. In the second episode, Du Sautoy explores how maths helped build imperial China and discovers how the symbol for the number zero was invented in India. He also looks at the Middle Eastern invention of algebra and how mathematicians such as Fibonacci spread Eastern knowledge to the West.