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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 human eye is a remarkable piece of precision engineering, but it is also extremely limited. Beyond the narrow range of light that makes up the familiar colours of the rainbow is a vast spectrum of light, entirely unseen. Richard Hammond does just that, using ground-breaking new imaging technologies to take the viewer on a breath-taking journey of discovery beyond the visible spectrum, seeing the world, quite literally, in a whole new light. From death-defying aerial repairmen in the United States using ultraviolet cameras to seek out an invisible force that lurks unseen on power lines, to German scientists unlocking the secrets of animal locomotion with the world's most powerful moving x-ray camera, to infrared cameras that can finally reveal the secrets within a humble beehive, he shows how new technologies are letting us see our world anew.

A jaguar fights to keep his river home in Brazil as the night brings both challenges and opportunities to hunt. Evening is falling in the world's greatest tropical wetland, Brazil's Pantanal. A stronghold for South America's most secretive big cat, the jaguar. And enjoying the last warmth of the day is a male known as Juru. At six years old and weighing over 100 kilos, he's amongst the largest, most powerful big cats in the Americas. This prime stretch of river has been his territory for two years. But tonight Juru's reign hangs in the balance. In a recent fight with a rival male, he badly injured his paw. It's left him weak and hungry. The coming days and nights will test him more than ever before. He'll need to summon the strength to defend his river.

In the third episode of the series, Commodus rises to power as Rome's new emperor, but not everyone supports his ascent. Among those conspiring against him: his older sister Lucilla.

In the fourth episode of the series, Commodus defeats his sister's coup but withdraws from governing, allowing others to amass power while he engages in an affair and banishes his wife.

In the fifth episode of the series, lavish imperial games at the Colosseum are highlighted by the emperor's bloody victories, but his paranoid abuses of power lead to a final betrayal.