Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.

Perfect for fans of Coraline and Roald Dahl, this fully-illustrated journey into the secret world of imaginary friends is quirky, dark, and utterly irresistible. Rudger is Amanda Shuffleup's imaginary friend. Nobody else can see Rudger-until the evil Mr. Bunting arrives at Amanda's door. Mr. Bunting hunts imaginaries. Rumor has it that he even eats them. And now he's found Rudger. Soon Rudger is alone, and running for his imaginary life. He needs to find Amanda before Mr. Bunting catches him-and before Amanda forgets him and he fades away to nothing. But how can an unreal boy stand alone in the real world? Featuring gorgeous illustrations and a beautiful design, this suspenseful fantasy tells a powerful tale of friendship, imagination, and remembering what you never knew you lost.

Abandoned by her mother and neglected by her scientist father, timid Elizabeth Murmur has only her fearless friend, Zenobia, for company. And Zenobia’s company can be very trying! When Elizabeth’s father takes them to live in his family home, Witheringe House, Zenobia becomes obsessed with finding a ghost in the creepy old mansion and forces Elizabeth to hold séances and wander the rooms at night. With Zenobia’s constant pushing, Elizabeth investigates the history of the house and learns that it does hold a terrible secret: Her father’s younger sister disappeared from the grounds without a trace years ago. Elizabeth and Zenobia is a wonderfully compelling middle-grade story about friendship, courage, and the power of the imagination.

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.

Imaginary friend Budo narrates this heartwarming story of love, loyalty, and the power of the imagination—the perfect read for anyone who has ever had a friend . . . real or otherwise Budo is lucky as imaginary friends go. He's been alive for more than five years, which is positively ancient in the world of imaginary friends. But Budo feels his age, and thinks constantly of the day when eight-year-old Max Delaney will stop believing in him. When that happens, Budo will disappear. Max is different from other children. Some people say that he has Asperger's Syndrome, but most just say he's "on the spectrum." None of this matters to Budo, who loves Max and is charged with protecting him from the class bully, from awkward situations in the cafeteria, and even in the bathroom stalls. But he can't protect Max from Mrs. Patterson, the woman who works with Max in the Learning Center and who believes that she alone is qualified to care for this young boy. When Mrs. Patterson does the unthinkable and kidnaps Max, it is up to Budo and a team of imaginary friends to save him—and Budo must ultimately decide which is more important: Max's happiness or Budo's very existence. Narrated by Budo, a character with a unique ability to have a foot in many worlds—imaginary, real, child, and adult— Memoirs of an Imaginary Friend touches on the truths of life, love, and friendship as it races to a heartwarming . . . and heartbreaking conclusion.

A TIME magazine Top 10 Children's Book of 2015! The whimsical "autobiography" of an imaginary friend who doesn't know he's imaginary--perfect for fans of The Miraculous Journey of Edward Tulane and Toy Story. Jacques Papier has the sneaking suspicion that everyone except his sister Fleur hates him. Teachers ignore him when his hand is raised in class, he is never chosen for sports teams, and his parents often need to be reminded to set a place for him at the dinner table. But he is shocked when he finally learns the truth: He is Fleur's imaginary friend! When he convinces Fleur to set him free, he begins a surprising and touching, and always funny quest to find himself—to figure out who Jacques Papier truly is, and where he belongs. “A charming story so easy to visualize that it feels like a future Pixar movie.”—The Wall Street Journal “A clever tale about finding purpose and self-acceptance”—Good Housekeeping