Requiring no more than a knowledge of high school mathematics and written in clear and accessible language, this book will give all readers a new insight into some of the most enjoyable and fascinating aspects of geometry. Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure holds many intriguing "secrets." For example, if a circle is inscribed in any random triangle and then three lines are drawn from the three points of tangency to the opposite vertices of the triangle, these lines will always meet at a common point-no matter what the shape of the triangle. This and many more interesting geometrical properties are revealed in this entertaining and illuminating book about geometry. Flying in the face of the common impression that mathematics is usually dry and intimidating, this book proves that this sometimes-daunting, abstract discipline can be both fun and intellectually stimulating. The authors, two veteran math educators, explore the multitude of surprising relationships connected with triangles and show some clever approaches to constructing triangles using a straightedge and a compass. Readers will learn how they can improve their problem-solving skills by performing these triangle constructions. The lines, points, and circles related to triangles harbor countless surprising relationships that are presented here in a very engaging fashion.

New York Times Best Seller! 1500 5-Star Reviews! From the author that brought you NEW YORK TIMES best selling books The Harbinger, The Mystery of the Shemitah, and The Paradigm selling over 3 MILLION copies Imagine if you discovered a treasure chest in which were hidden ancient mysteries, revelations from heaven, secrets of the ages, the answers to man’s most enduring, age-old questions, and the hidden keys that can transform your life to joy, success, and blessing…This is The Book of Mysteries.

Esther Gottesfeld is the last living survivor of the notorious 1911 Triangle Shirtwaist fire and has told her story countless times in the span of her lifetime. Even so, her death at the age of 106 leaves unanswered many questions about what happened that fateful day. How did she manage to survive the fire when at least 146 workers, most of them women, her sister and fiancé among them, burned or jumped to their deaths from the sweatshop inferno? Are the discrepancies in her various accounts over the years just ordinary human fallacy, or is there a hidden story in Esther's recollections of that terrible day? Esther's granddaughter Rebecca Gottesfeld, with her partner George Botkin, an ingenious composer, seek to unravel the facts of the matter while Ruth Zion, a zealous feminist historian of the fire, bores in on them with her own mole-like agenda. A brilliant, haunting novel about one of the most terrible tragedies in early-twentieth-century America, Triangle forces us to consider how we tell our stories, how we hear them, and how history is forged from unverifiable truths.

What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. The authors trace the appearance of the Golden Ratio throughout history, demonstrate a variety of ingenious techniques used to construct it, and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. Requiring no more than an elementary knowledge of geometry and algebra, the authors give readers a new appreciation of the indispensable qualities and inherent beauty of mathematics.

Two veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts. In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Découverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places. This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. In another example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid - that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd - but enlightening - results. Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science.

Faith Kelly has what it takes to extort what she needs from the country's Most Wanted—but when her new case takes its toll in intimate ways, it becomes the most dangerous one of her career. It's case officer Faith Kelly's job to protect criminals in exchange for information. But Daryn McDermott is another story—one that's challenging her professional and personal responsibility. The activist daughter of a powerful conservative senator, Daryn's not only linked to a terrorist bombing, but also to Faith's brother Sean, an Immigration and Customs Enforcement agent hired to bring her home. It's too late for that. When Daryn is found murdered near the Oklahoma City National Memorial, Sean runs—and Faith follows. He leads her into a web of private secrets and lies, a far-reaching conspiracy...and murder. Faith's past has returned with a vengeance, casting a shadow of doubt on everyone she trusts—and cutting into the very heart of everyone she loves.

An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.