Beautifully illustrated with old engravings as well as contemporary imagery, Sacred Number introduces basic counting systems; significant numbers from major religious texts; the importance of astronomy, geometry, and music to number quality; how numbers affect architecture. Lundy explains why the ideas of Pythagoras still resonate, and she profiles each number from one to ten to show its distinct qualities: why, for example, the golden section is associated with five, and seven with the Virgin Mary.

    Twenty-two years later, he did. April 1945 – Berlin. The world had been at war for more than five-and-a-half years – approximately seventy million people were dead across the globe. The epicentre of the twelve-year-old Third Reich was now surrounded, enveloped by bitter Soviet forces hardened by Nazi barbarity in the east over the last four years. As the buildings were blasted into rubble, pounded by Russian guns and bombs, before their troops and tanks, Hitler was hunkered down in his last headquarters – the dark and damp bunker under the Reich Chancellery. As the Third Reich began to crumble as fast as the city’s buildings, what was the state of mind of the tyrant? Only his closest and fanatical allies saw the collapse, none more so than Hitler’s servants, Otto Gunsche and Heinz Linge – two individuals which witnessed the final act of their regime. An act tinged over the last ten days in late April with selfish betrayal, increasingly forlorn hope, pleas, desperation and eventually suicide. As the Soviets closed in with impending vigour, in the concrete tomb below ground and under the thunderous booms of the petrifying battle for Berlin, the mind of the dictator disintegrated into drugs, delusion and a determination to die. Not by the enemy bullet but one of his own. This is the story of the people who held a unique place in world history – the ones who were there when the nightmare of Nazism and the horrors which accompanied it was finally banished as a dark chapter in the story of the human race.

    

    The calculus is not a hard subject and I prove this through an easy to read and obvious approach spanning only 100 pages. I have written this book with the following type of student in mind; the non-traditional student returning to college after a long break, a notoriously weak student in math who just needs to get past calculus to obtain a degree, and the garage tinkerer who wishes to understand a little more about the technical subjects. This book is meant to address the many fundamental thought-blocks that keep the average 'mathaphobe' (or just an interested person who doesn't have the time to enroll in a course) from excelling in mathematics in a clear and concise manner. It is my sincerest hope that this book helps you with your needs.Show more Show less

    This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

    Have foreigners shaped China’s history to a greater extent than has previously been acknowledged, reaching back possibly millennia? Was Confucius’ most famous book, the Analects, inspired by entheogenic medicines imported from abroad, possession of which in the 1930s brought one before the firing squad in the name of Confucius? In these book review essays by Isham Cook, foreign devils, old China Hands, eccentric expatriates, and a few Chinese tell an offbeat history of China’s last two centuries, with a backward glance at ancient China as told by Western mummies.

    All of the mentioned are just puppets on an invisible string doing the biddings of a few unseen puppeteers. Yes, that’s right. A few elite and undisclosed organizations send our children off to war, restrict the growth of the middle class, and limit educational opportunities for American citizens. The sad truth is this is nothing new. Thomas Jefferson and Benjamin Franklin warned of the dangers and destructive power of these elites if left unchecked. These few unchosen were able, and continue, to use the Federal Reserve Banking System, universities, and war to create economic recessions and depressions that provide unnoticed benefits to a select group of social manipulators. In this stunning new book, Mark Mullen takes us on an intellectual journey through the world of secret partnerships created by unfamiliar ideologues designed to acquire most of the nation’s wealth and power. In Who Controls America, Mullen shines a light on those few elites who place greed, power, and profits above the interests of the American citizen and the pursuit of the American Dream.

    In an era of the military space race, Erich von Däniken boldly proclaimed that Earth had been visited by more advanced beings early in our history. But prescientific man had no concept of space ships, so he called their vehicles “chariots,” and those driving the chariots became “gods.” Over the next five decades, von Däniken’s more than 40 books built an ever-stronger case for Earth being visited by extraterrestrial visitors. And Chariots became an international best seller, with 30 million copies sold in more than two dozen languages. Also during that time, the case for ET visitations millennia ago was being reexamined by contemporary UFO researchers, who found evidence of modern visitations. And von Däniken expanded his perspective to encompass the present. Now, he presents his long-awaited sequel to Chariots of the Gods, proclaiming that the gods never left us with all-new material to show that ancient aliens are still with us. The Gods Never Left Us contends that recent advancements in biotechnology, astrophysics, engineering, and artificial intelligence not only give us a fresh perspective on his ancient astronaut theory but actually validates it. We are—as a race—embarking on the exact same trajectory of our own interplanetary colonization, just as von Däniken suggested Earth itself was colonized. ETs are definitely at work today. And that affects all of us. Why do they do what they do? What could an extraterrestrial species possibly gain from observing us in the same way we look at ants? What have these strangers wanted for the past thousands of years? Can’t they leave us alone? And what makes it so difficult for us to acknowledge the existence of these extraterrestrials? That is what this book deals with. "Erich's newest book is a fascination journey from the ancient past into the present with a plethora of scientific evidence and documented research. As always, he ads his own "to the point" take on it all. Readers may also like that his newest work moves in a slightly different direction from his past books. A thoroughly enlightening and enjoyable Read." —Bruce Cunningham, Director, Ancient Mysteries International LLC & Publisher of Advanced Archaeology Review magazine

    No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like pi which never end. It literally never ends.The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the "imaginary" number i and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed: is it a number, or isn't it?How Numbers Work takes a tour of this mind-blowing but beautiful realm of numbers and the mathematical rules that connect them. Not only that, but take a crash course on the biggest unsolved problems that keep mathematicians up at night, find out about the strange and unexpected ways mathematics influences our everyday lives, and discover the incredible connection between numbers and reality itself. ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.

    Students, researchers, historians, specialists — in short, everyone with an interest in mathematics — will find it engrossing and stimulating.Beginning with the ancient Near East, the author traces the ideas and techniques developed in Egypt, Babylonia, China, and Arabia, looking into such manuscripts as the Egyptian Papyrus Rhind, the Ten Classics of China, and the Siddhantas of India. He considers Greek and Roman developments from their beginnings in Ionian rationalism to the fall of Constantinople; covers medieval European ideas and Renaissance trends; analyzes 17th- and 18th-century contributions; and offers an illuminating exposition of 19th century concepts. Every important figure in mathematical history is dealt with — Euclid, Archimedes, Diophantus, Omar Khayyam, Boethius, Fermat, Pascal, Newton, Leibniz, Fourier, Gauss, Riemann, Cantor, and many others.For this latest edition, Dr. Struik has both revised and updated the existing text, and also added a new chapter on the mathematics of the first half of the 20th century. Concise coverage is given to set theory, the influence of relativity and quantum theory, tensor calculus, the Lebesgue integral, the calculus of variations, and other important ideas and concepts. The book concludes with the beginnings of the computer era and the seminal work of von Neumann, Turing, Wiener, and others."The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature Magazine.

    Any word might be knocked and buffeted, subjected to twists and turns, expansions and contractions, happy and unhappy accidents. There are intriguing tales behind even the most familiar terms, and they can say as much about the present as they do the past.Busking, for instance, originally meant piracy. Grin meant to snarl. A bimbo was a man; nice meant ignorant; glamor was magic, and a cupboard was a table. Buxom used to mean obedient; a cloud was a rock; raunchy originally meant dirty.Focusing on one hundred surprising threads in the evolution of English, The Accidental Dictionary reveals the etymological origins and quirky developments that have led to the meanings we take for granted today. It is a weird and wonderful journey into words.So, let's revel in its randomness and delight in its diversity—our dictionary is indeed accidental.

    This cornucopia was devoted mainly to culture and the arts, the craft of writing, and travels to remote places, along with the movies, American popular song, email, multitasking, baseball, Central Park, Tina Brown, Pauline Kael, Steve Martin, and other complications of modern life. Written with elegance and humor, these pieces are now collected in The Writer Who Stayed."If you value vintage journalism of an old-fashioned vividness and integrity please, please read this book."—Wall Street Journal"Our 'endlessly supple' English language will, Zinsser says, 'do anything you ask it to do, if you treat it well. Try it and see.' Try him and see craftsmanship."—George F. Will"Zinsser—who, with On Writing Well, taught a whole lot of us how to set down a clean English sentence—last year won a National Magazine Award for his Friday web columns in The American Scholar. They're now in a collection that's completely charming, impeccably polished, and Strunk-and-White-ishly brief. He's the youngest 90-year-old you'll read this week."—New York MagazineWilliam Zinsser is a lifelong journalist and nonfiction writer—he began his career on the New York Herald Tribune in 1946—and is also a teacher, best known for his book On Writing Well, a companion held in affection by three generations of writers, reporters, editors, teachers, and students. His 17 other books range from memoir (Writing Places) to travel (American Places), jazz (Mitchell & Ruff), American popular song (Easy to Remember), baseball (Spring Training) and the craft of writing (Writing to Learn). During the 1970s he was at Yale University, where he was master of Branford College and taught the influential nonfiction workshop that would start many writers and editors on their careers. He has taught at the New School, in New York, his hometown, and at the Columbia University Graduate School of Journalism.

    This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

    

    The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.