The Golden Section—otherwise known as phi, the golden mean, or the golden ratio—is one of the most elegant and beautiful rations in the universe.Defined as a line segment divided into two unequal parts, such that the ratio of the shorter portion to the longer portion is the same as the ratio of the longer portion to the whole, it pops up throughout nature—in water, DNA, the proportions of fish and butterflies, and the number of teeth we possess—as well as in art and architecture, music, philosophy, science, and mathematics.Beautifully illustrated, The Golden Section tells the story of this remarkable construct and its wide-ranging impact on civilization and the natural world.

    While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world inwhich we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields.This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics andengineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.

    In this little book Welsh writer and artist David Wade paints a picture of one of the most elusive and pervasive concepts known to man.

    In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

     In fact, it may even be bigger than the Internet. It is such a profound paradigm shift in the technology of money that even experts on the topic are still trying to wrap their heads around it. Pandora's box has been opened and there is no going back. Bitcoin will forever transform society and its implications are beyond what we can even currently imagine. Bitcoin can be hard to grasp at first – and if someone has tried to explain it to you and you feel like you still don't get it, don't worry. This book will take you by the hand and explain to you in the simplest terms, using analogies, metaphors and illustrations what the essence of Bitcoin is and why you must pay attention to the revolution that is about to take place. In Bitcoin for Beginners you will find out: How the Bitcoin Technology works The difference between Bitcoin and Blockchain How mining works How to make money with Bitcoin The top myths about Bitcoin How Bitcoin will take over the world How to buy and sell Bitcoin What forks are And much more! DON'T HESITATE. TO START ON A JOURNEY THAT COULD DEEPLY TRANSFORM HOW YOU RELATE TO THE CONCEPT OF MONEY, SCROLL UP AND CLICK THE "BUY" BUTTON NOW!

    This is one of the most power-packed prosperity books around. Anyone can attract more money using simple metaphysical and mind power techniques, but advanced money attractors have a deeper grasp of the subtler spiritual truths underlying the money-manifesting process. You can attract a lot more money than you ever have before, and this book will give you the knowledge you need to be able to do it just as naturally as you now breathe.In fact, this life-changing little book will teach you that the money you want is actually here now, that it is a part of you, and that you already have it. Within these covers resides an astounding power, which will become increasingly apparent to you over time and with subsequent readings, and spurred on by this power, you can begin to turn your financial dreams into reality. Table of Contents: Secret One......: You Already Have ItSecret Two......: It Is Not Separate from YouSecret Three...: It Is Not in Your FutureSecret Four.....: It Is Right for You to Have ItSecret Five......: You Are Worthy of Having ItSecret Six........: A Higher You Wants ItSecret Seven...: Inspiration Beats PlanningSecret Eight.....: Be a Person Who Has ItSecret Nine......: Cooperate with the UniverseSecret Ten.......: Spread the Good AroundAttracting more money, manifesting wealth, creating a life of prosperity, abundance, and affluence—these are things anyone can accomplish, but relatively few do. The difference between the haves and the have nots? It’s a mental difference. It all starts in the mind, with the power of thought. This book will teach you how to think in a way that will raise you to glorious new heights of success, achievement, and financial freedom.

    Whereas Caesar Triumphant covers Caesar's invasion of the Isle of Wa, now known as Japan, Caesar Ascending is set in 44 BC and tells the story of his planned invasion of Parthia, and includes the characters of the internationally bestselling Marching With Caesar series, featuring Titus Pullus. Determined not to repeat the mistakes made by Caesar's friend and fellow Triumvir Marcus Licinius Crassus, the Dictator has trained his Legions in tactics specifically designed to thwart the famed Parthian cataphracts and horse archers, but as Caesar and his army learns, the Parthians have been working on their own surprises, all in an attempt to destroy another Roman army and send a message to Rome that they are not the only world power.

    This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

    But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    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.

    Packed with math activities and puzzles, compelling stories of math geniuses, math facts and stats, and more, How to be a Math Genius makes the dreaded subject of math both engaging and relevant.

    Topics include the development of counting and numbers systems, the emergence of zero, cultures that don’t have numbers, algebra, solid geometry, symmetry and beauty, perspective, riddles and problems, calculus, mathematical logic, friction force and displacement, subatomic particles, and the expansion of the universe. Great mathematical thinkers covered include Napier, Liu Hui, Aryabhata, Galileo, Newton, Russell, Einstein, Riemann, Euclid, Carl Friedrich Gauss, Charles Babbage, Montmort, Wittgenstein, and many more. The book is beautifully illustrated throughout in full color.

    Highly recommended for graduate-level libraries.' ChoiceThis highly successful text, which first appeared in the year 1972 and has continued to be popular ever since, has now been brought up-to-date by incorporating the remarkable developments in the field of 'phase transitions and critical phenomena' that took place over the intervening years. This has been done by adding three new chapters (comprising over 150 pages and containing over 60 homework problems) which should enhance the usefulness of the book for both students and instructors. We trust that this classic text, which has been widely acclaimed for its clean derivations and clear explanations, will continue to provide further generations of students a sound training in the methods of statistical physics.

    As you identify your tribe and divinely align in time with God's calendar, you will discover how to find your position in God's Kingdom, how to war effectively for your inheritance, and then walk in His blessings.A Time to Advance: Understanding the Significance of the Hebrew Tribes and Months will help you understand how God is developing His whole conquering army for today. You will also understand how each part moves together, and the redemptive quality of God's covenant plan for Israel. This will help ground you on how we are grafted into a movement in days ahead.As you learn how to think like God thinks and study the Hebrew tribes and months, you will receive prophetic understanding of how the Lord orders your steps throughout the year. You will also see your place in God's next Triumphant Reserve that is rising in the Earth today!