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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.

The Great Pyramid of Giza's construction is still shrouded in mystery, despite it being the only survivor among the Seven Wonders of the Ancient World. In Building the Great Pyramid, travel back 4,500 years with the BBC as they re-create the circumstances under which it may have been built, as well as the daily life of the population at that time. Expert archaeologists, Egyptologists, and scholars share their latest theories on what may have happened. The film combines dramatic reconstruction, location shooting and state-of-the-art CGI computer effects. Directed and written by Jonathan Stamp.

Washington, D.C. is in many ways a city of extremes. Starland Vocal Band, Marvin Gaye, Duke Ellington, Nils Lofgren, Chuck Brown, Henry Rollins, Fugazi and Trouble Funk all hail from D.C. In the early '70s, the music style go-go originated here, and has remained a local craze ever since. Dave Grohl sits down with Trouble Funk's Big Tony Fisher to talk about go-go, and explores its origins with Chuck Brown, the genre's undisputed godfather.
He also chats with Don Zientara, owner of Inner Ear Studios, which the Virginia-raised Grohl says 'produced the entire soundtrack of my youth,' as well as with members of the harDCore band Bad Brains and Ian MacKaye of Teen Idles, Minor Threat and Fugazi, who all recorded at Inner Ear over the decades. The song 'The Feast and the Famine' is recorded during this episode.

In the 1960s, US President John F Kennedy proposed landing a man on the moon before the decade was finished. This film has interviews with most of the surviving astronauts of the Apollo program who were making ready to make that great voyage with an army of experts determined to make the endeavour possible. Through training, tragedy and triumph, we follow the greatest moments of one of Humanity's great achievements. The documentary reviews both the footage and media available to the public at the time of the missions, as well as NASA films and materials which had not been opened in over 30 years.

Filmmaker Daniel McNicoll explores the emerging movement to reclaim the ancient medieval and renaissance martial arts in this documentary narrated by Welsh actor John Rhys-Davies, and produced on corroboration with Lord of the Rings director Peter Jackson. The Medieval and Renaissance blade was a remarkable weapon crafted with the utmost attention to detail. Though the history of the sword remains largely shrouded in mystery for younger moviegoers, their presence on the big screen can still be felt in the Star Wars saga, as well as films like Chronicles of Narnia and The Pirates of the Caribbean. Join host Davies as he traces the history of this remarkable weapon throughout the ages, in the process giving us a better understanding of the sword's unique role in both history, and films.

'Crude Awakening'- To combat the worst environmental disaster in American history, BP and the Coast Guard dumped nearly 2 million gallons of a chemical dispersant called Corexit into the Gulf. But instead of helping clean up the spill, Corexit made things worse. Shane Smith heads to Louisiana to report on the lasting effects of the BP oil spill. 'The Enemy of My Enemy' - Yemen, the fractured state in the Arabian peninsula, is at the top of the worry list for President Obama's national security team, and the rise of Al Qaeda there is only half the reason why. The real trouble is a current threat posed by the little-known Houthi rebel movement in the north of the country - a grassroots army, allegedly funded by Iran, that has never granted access to any other Western film crew before. Ben Anderson goes deep into Houthi-controlled territory to learn about the group that's fighting, and beating, Al Qaeda in the east, Saudi Arabia in the north, and Yemen's central government in the south.