Al-Khalili travels to northern Syria to discover how, a thousand years ago, the great astronomer and mathematician Al-Biruni estimated the size of the earth to within a few hundred miles of the correct figure. He discovers how medieval Islamic scholars helped turn the magical and occult practice of alchemy into modern chemistry. In Cairo, he tells the story of the extraordinary physicist Ibn al-Haytham, who helped establish the modern science of optics and proved one of the most fundamental principles in physics - that light travels in straight lines. Prof Al-Khalili argues that these scholars are among the first people to insist that all scientific theories are backed up by careful experimental observation, bringing a rigour to science that didn't really exist before.

Dan Snow uncovers the lost Vikings in America with space archaeologist Dr Sarah Parcak. Sarah uses satellites 383 miles above the earth to spot ruins as small as 30cm buried beneath the surface. As Sarah searches for Viking sites from Britain to America, Dan explores how they voyaged thousands of miles when most ships never left the shoreline. He also tracks their expansion west, first as raiders and then as settlers and traders throughout Britain and beyond to Iceland and Greenland. In North America they excavate what could be the most westerly Viking settlement ever discovered.

This is the story of a book that could have changed the history of the World. To the untrained eye, it is nothing more than a small and unassuming Byzantine prayer book. For faintly visible beneath the prayers on its pages are other, unique, writings - words that have been lost for nearly two thousand years. The text is the only record of work by one of the world's greatest minds - the ancient Greek, Archimedes - a mathematical genius centuries ahead of his time. Hidden for a millennium in a middle eastern library, it has been written over, broken up, painted on, cut up and re-glued. But in the nick of time scientists have saved the precious, fragile document, and for the first time it is revealing just how revolutionary Archimedes' ideas were. If it had been available to scholars during the Renaissance, we might have reached the Moon over a hundred years ago.

Every year, over a thousand climbers try to reach the summit of Mount Everest, with the annual record for successful attempts currently standing at 633. But of that number, nearly half were Sherpas - the mountain's unsung heroes. Yet the Sherpa community has remained secretive about their nation, culture and experiences living in the shadow of the world's highest mountain. Now, for the first time, they open the door into their world. Without the expertise of the Sherpas, only the hardiest and most skilful climbers would succeed. Every day they risk their lives for the safety of others, yet they seek neither glory nor reward, preferring to stay in the background. Following the stories of four such Sherpas - Phurba, Ngima, Ngima Tenji and Gelu - this film reveals the reality of their daily lives, not just up the mountain, but with their families after they return home.

In the fourth part of the series, Diarmaid MacCulloch makes sense of the Reformation, and of how a faith based on obedience and authority gave birth to one based on individual conscience. He shows how Martin Luther wrote hymns to teach people the message of the Bible, and how a tasty sausage became the rallying cry for Swiss Reformer Ulrich Zwingli to tear down statues of saints, allow married clergy and deny that communion bread and wine were the body and blood of Christ.

In the third part of his journey into the history of Christianity, Professor Diarmaid MacCulloch charts Orthodoxy's extraordinary fight for survival. After its glory days in the eastern Roman Empire, it stood right in the path of Muslim expansion, suffered betrayal by crusading Catholics, was seized by the Russian tsars and faced near-extinction under Soviet communism. MacCulloch visits the greatest collection of early icons in the Sinai desert, a surviving relic of the iconoclastic crisis in Istanbul and Ivan the Terrible's cathedral in Moscow to discover the secret of Orthodoxy's endurance.