From space, Earth is a kaleidoscope. Turquoise plankton blooms trigger a feeding frenzy, China turns yellow with rapeseed flowers, and mysterious green lights appear in the ocean. Satellites give us a new perspective on its greatest and most beautiful spectacles allowing us to make new discoveries We can watch landscapes change through the seasons and marvel in the scale of their transformations.
Satellite cameras capture a kaleidoscope of extraordinary colours surprising and constantly changing, created by natural phenomena, by animals and by people. These colours are revealing new insight into the health of our fragile planet, transforming our understanding of our colourful home.

Mathematician Dr Hannah Fry explores the mystery of maths. It underpins so much of our modern world that it's hard to imagine life without its technological advances, but where exactly does maths come from? Is it invented like a language or is it something discovered and part of the fabric of the universe? It's a question that some of the most eminent mathematical minds have been wrestling with. To investigate this question, Hannah goes head first down the fastest zip wire in the world to learn more about Newton's law of gravity, she paraglides to understand where the theory of maths and its practice application collide, and she travels to infinity and beyond to discover that some infinities are bigger than others.
In this episode, Hannah goes back to the time of the ancient Greeks to find out why they were so fascinated by the connection between beautiful music and maths. The patterns our ancestors found in music are all around us, from the way a sunflower stores its seeds to the number of petals in a flower. Even the shapes of some of the smallest structures in nature, such as viruses, seem to follow the rules of maths. All strong evidence for maths being discovered. But there are those who claim maths is all in our heads and something we invented. To find out if this is true, Hannah has her brain scanned. It turns out there is a place in all our brains where we do maths, but that doesn't prove its invented.
Experiments with infants, who have never had a maths lesson in their lives, suggests we all come hardwired to do maths. Far from being a creation of the human mind, this is evidence for maths being something we discover. Then along comes the invention of zero to help make counting more convenient and the creation of imaginary numbers, and the balance is tilted in the direction of maths being something we invented. The question of whether maths is invented or discovered just got a whole lot more difficult to answer

The story of the British Library's Royal Manuscripts collection reaches its end with the last great flowering of illumination, in the magnificent courts of the Tudors. Dr Janina Ramirez investigates astrological texts created for Henry VII, and unwraps his will - still in its original, extravagantly-decorated velvet and gold cover. She hears music written for Henry VIII, which went unperformed for centuries; and reads love notes between the king and Anne Boleyn, written in the margins of a prayer book. Nina also visits Bruges, the source of many of the greatest manuscripts, where this medieval art form collided with the artistic innovations of the Renaissance.

In the second episode, Professor Iain Stewart discovers how flowers have transformed our planet. He journeys to the remote islands of the South Pacific to track down the earliest flowers. In the deserts of Africa and rainforests of Vietnam, he sees how they brought brilliant colour to the most barren landscapes and sculpted the earth itself. And he learns how they drove the evolution of all animals - kick-starting our human story.

Written and presented by David Attenborough, who said: 'One of the most wonderful things about filming plants is that you can reveal hidden aspects of their lives, you can capture the moment as one plant strangles another, and as they burst into flower. But whilst time-lapse photography allows you to see things that no human being has ever seen before". David begins his journey inside the magnificent Palm House, a unique global rainforest in London. Here, he explores the extraordinary plants that are so well adapted to wet and humid environments and unravels the intimate relationships between wet zone plants and the animals that depend on them. It was in the wet zones of the world that plants first moved on to land and in the Waterlily House David reveals how flowers first evolved some 140 million years ago. Watching a kaleidoscope of breath-taking time-lapses of these most primitive of flowers swelling and blooming in 3D, he is able to piece together the very first evolutionary steps that plants took to employ a wealth of insects to carry their precious pollen for the first time. David discovers clues to answer a question that even had Charles Darwin stumped: how did flowering plants evolve so fast to go on to colonise the entire planet so successfully?

The fifth programme explores the alliances formed between the animal and plant worlds. Attenborough dives into Australia's Great Barrier Reef and contrasts the nocturnal feeding of coral, on microscopic creatures, with its daytime diet of algae. Some acacias are protected by ants, which will defend their refuge from any predator. Besides accommodation, the guards are rewarded with nectar and, from certain species, protein for their larvae as well. Fungi feed on plants but can also provide essential nutriment to saplings (Mycorrhiza). The connection is never broken throughout a tree's life and a quarter of the sugars and starches produced in its leaves is channelled back to its fungal partners. Meanwhile, fungi that feed on dead wood leave a hollow trunk, which also benefits the tree. Orchids enjoy a similar affiliation. Lichens are the product of a relationship between fungi and a photosynthetic associate, usually algae. They are extremely slow-growing, and a graveyard is the perfect location to discover their exact longevity. Mistletoe is a hemiparasite that obtains its moisture from a host tree, while using own leaves to manufacture food. Its seeds are deposited on another by the mistletoe tyrannulet, following digestion of the fruit. The dodder (Cuscuta) is also parasitic, generally favouring nettles, and siphons its nourishment through periodic 'plugs' along its stem. The rafflesia has no stem or leaves and only emerges from its host in order to bloom — and it produces the largest single flower: one metre across.