Fractals - The Colors Of Infinity

Arthur C. Clarke, through interviews with scientists and mathematicians like Benoit Mandlebrot, use the popular Mandlebrot Set to explore how easy formulas can bring about intricate results. It is also used in an attempt to answer questions about the longevity of the universe.




Benoit Mandelbrot discovered what is now called the M-Set in the early seventies and coined the term fractal to describe the geometry behind it. The power and the beauty of fractals were only capable of being seen with the advent of computers, which become psychedelic windows on the infinite when using simple fractal equations.

In 1992 Nigel Lesmoir-Gordon made the TV documentary, The Colors of Infinity about the Mandelbrot Set and fractals, which has since been seen right round the world. Nigel s enthusiasm brought together a dream team of contributors for the film who all now contribute to the book tracking how fractals have developed since the film was made. Sir Arthur C Clarke presented the film and in the book gives a lucidly simple account of the mathematics of the M-Set.

Hunting the Hidden Dimension

You may not know it, but fractals, like the air you breathe, are all around you. Their irregular, repeating shapes are found in cloud formations and tree limbs, in stalks of broccoli and craggy mountain ranges, even in the rhythm of the human heart.




This film takes viewers on a fascinating quest with a group of maverick mathematicians determined to decipher the rules that govern fractal geometry. For centuries, fractal-like irregular shapes were considered beyond the boundaries of mathematical understanding. Now, mathematicians have finally begun mapping this uncharted territory.

Their remarkable findings are deepening our understanding of nature and stimulating a new wave of scientific, medical, and artistic innovation stretching from the ecology of the rain forest to fashion design. The documentary highlights a host of filmmakers, fashion designers, physicians, and researchers who are using fractal geometry to innovate and inspire.

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The Story of Maths

Four-part series about the history of mathematics, presented by Oxford professor Marcus du Sautoy. This series is currently only available on Veoh, so my apologies to those that have issues with Veoh. I will post alternative links as soon as they become available.

After showing how fundamental mathematics is to our lives, du Sautoy explores the mathematics of ancient Egypt, Mesopotamia and Greece. In Egypt, he uncovers use of a decimal system based on ten fingers of the hand, while in former Mesopotamia he discovers that the way we tell the time today 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, Euclid, Archimedes and Pythagoras, who is credited with beginning the transformation of mathematics from a tool for counting into the analytical subject we know today.

PART ONE

Watch The Story of Maths Part 1 | View More Free Videos Online at Veoh.com

PART TWO

Watch math 2-1.avi | View More Free Videos Online at Veoh.com




Watch math 2-2 | View More Free Videos Online at Veoh.com

PART THREE

Watch The Story of Maths ep03 The Frontiers of Space.WnA.avi | View More Free Videos Online at Veoh.com

PART FOUR

Watch The Story of Maths ep04 To Infinity and Beyond.WnA.avi | View More Free Videos Online at Veoh.com

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Fermat's Last Theorem

Simon Singh and John Lynch's film tells the enthralling and emotional story of Andrew Wiles. A quiet English mathematician, he was drawn into maths by Fermat's puzzle, but at Cambridge in the '70s, FLT was considered a joke, so he set it aside. Then, in 1986, an extraordinary idea linked this irritating problem with one of the most profound ideas of modern mathematics: the Taniyama-Shimura Conjecture, named after a young Japanese mathematician who tragically committed suicide.




The link meant that if Taniyama was true then so must be FLT. When he heard, Wiles went after his childhood dream again. "I knew that the course of my life was changing." For seven years, he worked in his attic study at Princeton, telling no one but his family. "My wife has only known me while I was working on Fermat", says Andrew.




In June 1993 he reached his goal. At a three-day lecture at Cambridge, he outlined a proof of Taniyama - and with it Fermat's Last Theorem. Wiles' retiring life-style was shattered. Mathematics hit the front pages of the world's press. Then disaster struck. His colleague, Dr Nick Katz, made a tiny request for clarification. It turned into a gaping hole in the proof. As Andrew struggled to repair the damage, pressure mounted for him to release the manuscript - to give up his dream. So Andrew Wiles retired back to his attic. He shut out everything, but Fermat.

A year later, at the point of defeat, he had a revelation. "It was the most important moment in my working life. Nothing I ever do again will be the same." The very flaw was the key to a strategy he had abandoned years before. In an instant Fermat was proved; a life's ambition achieved; the greatest puzzle of maths was no more.

Infinite Secrets - The Genius of Archimedes

In 1991, a small Medieval prayer book was sold at auction. Miraculously, some original writings of Archimedes, the brilliant Greek mathematician, were discovered hidden beneath the religious text. Through scholarly detective work with the help of modern technology, this book now reveals Archimedes’ stunningly original concepts, ideas, and theories—revelations that, if known sooner, might have reshaped our world.

Many historic figures have been hailed as ahead of their time. Few—if any—are said to be centuries ahead of their time. The Einstein of his era, Archimedes had a sophisticated understanding of mathematics, and designed marvelous war machines for his native Syracuse to use against the invading Romans. Many of Archimedes’ works disappeared during the Middle Ages, but some survived to help inspire the scientific revolution in the sixteenth and seventeenth centuries.

One document that seemed irretrievably lost was his final treatise The Method, which reputedly explained how he achieved his brilliant results—secrets he revealed nowhere else. Now, over 2200 years later, the discovery of The Method has experts and scientists dreaming of what might have been if Renaissance thinkers and other great minds had known of his ideas and been able to build on them

This documentary explores Archimedes’ rare writings, as well as the book’s mysterious beginnings, tumultuous history and amazing discovery. As the ancient text comes back from the dead, it unlocks its revolutionary contents—the infinite secrets of one of history’s greatest thinkers.

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Dangerous Knowledge

In this one-off documentary, David Malone looks at four brilliant mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing - whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide.




The film begins with Georg Cantor, the great mathematician whose work proved to be the foundation for much of the 20th-century mathematics. He believed he was God's messenger and was eventually driven insane trying to prove his theories of infinity.

PART ONE

Ludwig Boltzmann's struggle to prove the existence of atoms and probability eventually drove him to suicide. Kurt Gödel, the introverted confidant of Einstein, proved that there would always be problems which were outside human logic. His life ended in a sanatorium where he starved himself to death.




Finally, Alan Turing, the great Bletchley Park code breaker, father of computer science and homosexual, died trying to prove that some things are fundamentally unprovable.

The film also talks to the latest in the line of thinkers who have continued to pursue the question of whether there are things that mathematics and the human mind cannot know. They include Greg Chaitin, mathematician at the IBM TJ Watson Research Center, New York, and Roger Penrose.

PART TWO

Dangerous Knowledge tackles some of the profound questions about the true nature of reality that mathematical thinkers are still trying to answer today.

The Story of One

The story of the number one is the story of Western civilization. Terry Jones ("Monty Python's Flying Circus") goes on a humor-filled journey to recount the amazing tale behind the world's simplest number. Using computer graphics, "One" is brought to life, in all his various guises, in STORY OF 1, airing on PBS Wednesday, March 29, 2006, 8:00-9:00 p.m. ET. One's story reveals how celebrated civilizations in history were achieved, where our modern numbers came from and how the invention of zero changed the world forever - and saved us from having to use Roman numerals today.

How old is One? A precise answer is impossible, but a notched bone (called the Ishango bone) found in the Congo proves that he's been around for at least 20,000 years. His life really took off 6,000 years ago, when the Sumerians turned him into a cone-shaped token and then into the first-ever numeric character, invention that made arithmetic - and therefore city life - possible, providing the means to assess wealth, calculate profits and loss, and, perhaps most important, collect taxes.

A thousand years later in Egypt, time-traveler Jones witnesses the first use of "million," as well as the invention of formal measurement: Egyptians create their own version of one, the cubit. Without the cubit, some of the wonders of the world might have been ... a little less wonderful. STORY OF 1 gives the viewer a glimpse of how a cubit-challenged pyramid would look.

Then it's on to ancient Greece, where One was held in high regard. However, his biggest fan, Pythagoras, lost his mind studying him, and the renowned Archimedes was so absorbed in diagrams that he lost his life to an invading Roman. The Romans slew One, too; they had no time for theoretical mathematics. In his new incarnation, "I" became a tool for imposing order.

Unwieldy though they were, Roman numerals would dominate Europe for the next 2,000 years. Jones discovers how the numbers we use today eventually managed to supplant them, making it much easier for us to subtract MDCCLVIII from MDCCCXLIV. It all begins in India, where the symbols for one through nine were invented and where Jones tracks down the first use of "zero." Here, STORY OF 1 takes a romantic turn. In Zero, One found his perfect mate. It was a union that would change the world.

Then it's on to Baghdad, where Jones discovers that Muslem scholars were smitten with One and Zero - and two through nine as well. The most famous Muslim scholar, Al-Khwarizmi, and his colleagues taught these performing numerals a whole set of new tricks, feats that enabled science, mathematics and astronomy to reach new heights in the Middle East.

The Indian numbers were a smash hit across the Islamic world before they were finally brought to Europe, where they met fierce resistance. It took 500 years for the battle between Roman and Indian numbers to play out, but by the 16th century, the Indian figures, now commonly called Arabic numerals, finally triumphed - perhaps because Florentine mathematician Fibonacci showed Christian merchants how useful Indian numerals could be, for instance, for calculating profits.

But the story doesn't end there. Within a hundred years, German mathematician Gottfried Leibniz invented a binary system, using the Adam and Eve of mathematics, One and Zero. Since then, as the language of computers, this two-digit binary system has come to dominate every part of modern life.

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