Few sounds are more beautiful or moving than the underwater songs of the humpback whale. Male whales compete with their songs, which often last for 10 minutes at a time, and can be repeated for hours on end. Whales separated by thousands of miles of sea will sing almost identical songs. Researchers have found that the songs change throughout the breeding months, following a mysterious pattern repeated across the waves. Whales also use sound to hunt. To catch herring, humpback whales release a stream of bubbles to form a shimmering, circular fishing net. Emitting a repetitive loud scream, they scare the fish into a tight ball, then lunge out of the water to swallow the shoal whole. Now it seems that the long-held image of the gentle giant must change to one of a ferocious and opportunistic hunter.

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.

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.

An apocryphal view on the pyramids, starting in awe at the amazing achievement of the Pharaonic architecture and sculpture, most specially at Gizeh, given Cheops's pyramid's size, weight, incredibly precise carving, four pairs of slightly shifted half sides, stunningly precisely measured shapes and symmetry. Then it questions and challenges conventional Egyptology beliefs, which it calls unproven or even impossible to verify, such as the absence of machines, a wharf duration of only 20 years or accidental equinox-orientation. Next it elaborates the theory that other major pyramid technology sites in Precolombian America, Easter Island and China can't coincidentally lie on two lines intersecting at Gizeh, even if not contemporaneous and without known contacts in their ages, and have several improbable things in common, like some of their cultures. Elaborate mathematical theories and measurements indicate the Egyptians must have known some astronomy, pi and the golden number

Narrated by Ewan McGregor, Humpback Whales is an extraordinary journey into the mysterious world of one of nature's most awe-inspiring marine mammals. Set in the spectacular waters of Alaska, Hawaii and the remote islands of Tonga, this ocean adventure offers audiences an up-close look at how these whales communicate, sing, feed, play and take care of their young. Humpbacks were nearly driven to extinction 50 years ago, but today are making a slow but remarkable recovery. Join a team of researchers as they unlock the secrets of the humpback and find out why humpbacks are the most acrobatic of all whales, why they sing their haunting songs, and why these intelligent 55-foot, 50-ton animals migrate up to 10,000 miles round-trip every year.

Ewan McGregor and Charley Bormann are very close to finishing their journey. Discussions on security are still on the agenda; they cannot travel at night due to dangerous cartels. They will need to do many miles on a bus with space for the bikes inside. The team manage to get the bikes on after concerns they wouldn’t fit. Repairing and conditioning the bus is an achievement considering they did it in a few days.
Ewan and Charley get back on their bikes, and they head to their last border cross to enter the United States. After 12 hours in the border, the crew, Ewan and Charley make it to America. It’s an easy stretch to L.A. on their bikes. Ewan, the crew and family, finish the last leg. It’s done, they’ve managed to finish Long Way Up. It’s such an achievement. Episode 11 is a heartfelt finale, showcasing the end of an incredible journey from both Ewan, Charley, and the team that supported them.