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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.

Intelligence and adaptability allow primates to tackle the many challenges of life, and this is what makes our closest relatives so successful. This resourcefulness has enabled primates to conquer an incredible diversity of habitat. Hamadryas baboons live on the open plains of Ethiopia in groups up to 400 strong. Strength in numbers gives them some protection from potential predators. But, should their path cross with other baboon troops, it can lead to all-out battle, as males try to steal females from one another, and even settle old scores. Japanese macaques are the most northerly-dwelling primates and they experience completely different challenges. Some beat the freezing conditions by having access to a thermal spa in the middle of winter. But this privilege is only for those born of the right female bloodline. For western lowland gorillas, it's the male silverback that leads his family group in the rich forests of the Congo basin. He advertises his status to all with a powerful chest-beating display. Most primates are forest dwellers, and one of the strangest is the tarsier – the only purely carnivorous primate. As it hunts for insects the tarsier leaps from tree to tree in the dead of night, using its huge forward-facing eyes to safely judge each jump. Good communication is essential for success in primate society.

The second programme deals with the mechanics of flight. Getting into the air is by far the most exhausting of a bird's activities, and Sir Attenborough observes shearwaters in Japan that have taken to climbing trees to give them a good jumping-off point. The albatross is so large that it can only launch itself after a run-up to create a flow of air over its wings. A combination of aerodynamics and upward air currents (or thermals), together with the act of flapping or gliding is what keeps a bird aloft. Landing requires less energy but a greater degree of skill, particularly for a big bird, such as a swan. Weight is kept to a minimum by having a beak made of keratin instead of bone, a light frame, and a coat of feathers, which is maintained fastidiously. The peregrine falcon holds the record for being fastest in the air, diving at speeds of over 300 km/h. Conversely, the barn owl owes its predatory success to flying slowly, while the kestrel spots its quarry by hovering. However, the true specialists in this regard are the hummingbirds, whose wings beat at the rate of 25 times a second. The habits of migratory birds are explored. After stocking up with food during the brief summer of the north, such species will set off on huge journeys southwards. Some, such as snow geese, travel continuously, using both the stars and the sun for navigation. They are contrasted with hawks and vultures, which glide overland on warm air, and therefore have to stop overnight.

In late Cretaceous Canada, in what will be known as Dinosaur Provincial Park, a Daspletosaurus stalks a Chasmosaurus in a forest, but loses the element of surprise and is forced to retreat. The Chasmosaurus comes across a younger Daspletosaurus, before being ambushed by a group of the tyrannosaurids. The episode then cuts to the high Arctic, where Edmontosaurus are hunted by a large species of Troodon. The theropods attack at night, separating a juvenile from the herd and severely wounding it, only to be driven away by an adult. In the morning, they return to eat the carcass of the juvenile, which died during the night. The episode returns to the Daspletosaurus, who chase and bring down the Chasmosaurus. The larger adults bully the youngsters off the carcass, forcing them to wait until they have finished. The episode then cuts to Madagascar, where a mother Majungasaurus (an Abelisaurid) and her two offspring chase a group of Rahonavis off a carcass. However, they are temporarily driven off themselves by a male Majungasaurus. But, after he steals some food from one of the young, the female attacks him, before she and her young cannibalise his body. The episode returns once again to North America, where the Daspletosaurus are waiting for the annual migration of Centrosaurus. They attack during a rainstorm, killing some of the ceratopsians. The Centrosaurus make it to a flooded river and begin to swim across, and although many make it to the other side, some are caught by giant crocodilians or are severely wounded by floating debris and thus drown, or drown for unseen reasons. In the morning, the carcasses attract scavengers, including the Daspletosaurus. A montage is then shown of Daspletosaurus and Majungasaurus, the narrator saying that together, the tyrannosaurids and abelisaurids were the last of the killer dinosaurs.

In Bhutan, Palin finds himself back in the land of yaks for a last look at the high Himalaya. Trekking to Chomolhari base camp he meets a nomad with a penchant for yak songs before heading down to Paro to witness the Buddhist festival or Tsechu. In a bar in Thimphu, he discusses reincarnation and the pursuit of happiness with Benji and Khendum, two of the king's cousins, and en route to Bangladesh is taken by Benji to see the rare black-neck cranes. On his journey south through Bangladesh, Michael visits the ship-breaking beaches of Chittagong and grid-locked Dhaka. He meets a man who made a fortune in Birmingham in the poultry business, and a woman who lends money only to women. On a 1920s paddle steamer he is serenaded with the words of Bengal's Shakespeare, and he completes his epic Himalayan journey aboard a fishing boat that carries him out into the Bay of Bengal and a westering sun.

The magnificent ancient city of pyramids at Caral in Peru is a thousand years older than the earliest known civilisation in the Americas and, at 2,627 BC, is as old as the pyramids of Egypt. Many now believe it is the fabled missing link of archaeology - a 'mother city'. If so, then these extraordinary findings could finally answer one of the great questions of archaeology: why did humans become civilised?" For over a century, archaeologists have been searching for what they call a mother city. Civilisation began in only six areas of the world: Egypt, Mesopotamia, India, China, Peru and Central America. In each of these regions people moved from small family units to build cities of thousands of people. They crossed the historic divide, one of the great moments in human history. Why? To find the answer archaeologists needed to find a mother city - the first stage of city-building. Caral, is so much older than anything else in South America that it is a clear candidate to be the mother city. It also is in pristine condition. Nothing has been built on it at all. Instead laid out before the world is an elaborate complex of pyramids, temples, an amphitheatre and ordinary houses. Scientists developed a number of theories. Some said it was because of the development of trade, others that it was irrigation. Some even today believe it was all because of aliens. Gradually an uneasy consensus emerged. The key force common to all civilisations was warfare. Crucially, there is not the faintest trace of warfare at Caral; no battlements, no weapons, no mutilated bodies. Instead, Ruth's findings suggest it was a gentle society, built on commerce and pleasure. In one of the pyramids they uncovered beautiful flutes made from condor and pelican bones. They have also found evidence of a culture that took drugs and perhaps aphrodisiacs. Most stunning of all, they have found the remains of a baby, lovingly wrapped and buried with a precious necklace made of stone beads.