'Flexing' is a dance style forged in far east Brooklyn, at the dead-end of a handful of subway lines. Flex dancers channel the grittiness and crime of East New York into choreographed violence with gun movements, simulated bone-breaking, and the mimicked ripping of hearts from opponent's chests. Through battles dancers gain respect, craft an artistic identity, and sometimes find a sanctuary from the poverty and violence that saturates their neighborhood. No other style of street-dance is this violent, scary, or beautifully theatrical. In this purely do-it-yourself scene, creativity and ambition bring a community together around frequent dance-battle showcases that have begun to attract an international audience and may catapult the best dancers into careers in theater or film. Following a group of dancers for over two years, Flex is Kings explores the hopes and realities of this under-acknowledged and totally unfunded group of urban artists

Iain Stewart investigates a new and controversial energy rush for the natural gas found deep underground. Getting it out of the ground involves hydraulic fracturing - or fracking. We travel to America to find to find out what it is, why it is a potential game changer and what we can learn from the US experience". Sometimes, this is right under the places people live in. He meets some of the people who have become rich from fracking as well as the communities worried about the risks. Director Jeff Wilkinson

In 1985, two adventurous young mountaineers, Joe Simpson and Simon Yates, set off to climb the treacherous west face of the Siula Grande in the Peruvian Andes. They were experienced climbers, and climbed "Alpine-style," climbing the mountain in "one great push," without setting up ropes or base camps ahead of time. After dealing with a snowstorm and some dangerous climbing over powder formations, they reached the summit (about 21,000 feet) on the third day. The climb down proved to be far more difficult. Simpson fell and broke his leg badly. Yates decided to try to lower Simpson down the mountain, one 300-foot section of rope at a time. The climbers had run out of gas to melt snow, so they couldn't risk stopping as night came, and a violent snowstorm began. Their plodding, painful journey hit a snag when Yates inadvertently lowered Simpson over the edge of a cliff. In the storm, the men couldn't hear each other's cries, and, Yates, uncertain as to Simpson's position, and gradually sliding down the slope himself, decided to cut the rope that connected them, sending Simpson plummeting to certain death. Miraculously, Simpson survived the fall, and was faced with the prospect of getting off the mountain alone with no food, no water, and a broken leg. In Touching the Void, filmmaker Kevin Macdonald (One Day in September) tells their story, based on Simpson's book, using contemporary interviews with the two men, and a reenactment of their climb and descent, featuring Brendan Mackey as Simpson and Nicholas Aaron as Yates

In the third episode we will see Europe by the 17th century taking over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss. Du Sautoy proceeds to describes René Descartes realisation that it was possible to describe curved lines as equations and thus link algebra and geometry. He talks with Henk J. M. Bos about Descartes. He shows how one of Pierre de Fermat’s theorems is now the basis for the codes that protect credit card transactions on the internet. He describes Isaac Newton’s development of math and physics crucial to understanding the behaviour of moving objects in engineering. He covers the Leibniz and Newton calculus controversy and the Bernoulli family. He further covers Leonhard Euler, the father of topology, and Gauss' invention of a new way of handling equations, modular arithmetic. The further contribution of Gauss to our understanding of how prime numbers are distributed is covered thus providing the platform for Bernhard Riemann's theories on prime numbers. In addition Riemann worked on the properties of objects, which he saw as manifolds that could exist in multi-dimensional space.

With optional Hebrew subtitles. The story of medieval Jews struggling to preserve their identity--and sometimes their lives--under the rule of Christianity and Islam. Whether labelled 'Christ-killers' by the Christians or 'dhimmi' (non-Muslim citizens of an Islamic community) by the Muslims, diaspora Jews built new lives and invented new ways of being Jewish in exile in the face of discrimination, blood-libels and persecution interspersed with periods of tolerance, protection and peaceful co-existence. Drawing on some of the documents they left behind, this episode offers a vivid portrait of Jewish bankers, merchants, doctors, poets and artists flourishing in Lincoln, Cordoba, Venice and Cairo and tells the story of their mass expulsion from Spain in 1492.

It's a timeless classic of children's literature and the third most-quoted book in English after the Bible and Shakespeare. But what lies behind the extraordinary appeal of Alice's Adventures in Wonderland to generations of adults and children alike? To mark the 150th anniversary of its publication, this documentary explores the life and imagination of the man who wrote it, the Reverend Charles Dodgson, better known as Lewis Carroll." Broadcaster and journalist Martha Kearney delves into the biographies of both Carroll himself and of the young girl, Alice Liddell, who inspired his most famous creation. Kearney's lifelong passion for Carroll's work began as a young girl, when she starred as Carroll's heroine Alice in her local village play. She discusses the book with a range of experts, biographers and distinguished cultural figures - from the actor Richard E Grant to children's author Philip Pullman - and explores with them the mystery of how a retiring, buttoned-up and meticulous mathematics don, who spent almost his entire life within the cloistered confines of Christ Church Oxford, was able to capture the world of childhood in such a captivating way