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.

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.

Rudger is Amanda's best friend. He doesn't exist, but nobody's perfect. Only Amanda can see her imaginary friend – until the sinister Mr Bunting arrives at Amanda's door. Mr Bunting hunts imaginaries. Rumour says that he eats them. And he's sniffed out Rudger. Soon Rudger is alone, and running for his imaginary life. But can a boy who isn't there survive without a friend to dream him up? A brilliantly funny, scary and moving read from the unique imagination of A.F. Harrold, this beautiful book is astoundingly illustrated with integrated art and colour spreads by the award-winning Emily Gravett.

From author and artist John Byrne comes another perspective on the development of both Superman and Batman that begins in 1942 and progresses right through to 2019.

"Enter the wildly inventive world of Imaginary Numbers, in which a marvelous roster of acclaimed writers conjure up magical happenings, fantastic visions, and brainteasing puzzles, all based in some way on mathematical ideas. This anthology offers a connoisseur's selection of a special brand of creative writing in which the authors play with a vast array of mathematical notions - from the marvels of infinity to the peculiarities of space-time to quantum weirdness, the relativity of time, and the curious attraction of black holes." --Book Jacket.

A history of modern painting, presented through the story of the Mona Lisa, features an artist who serves as a museum tour guide introducing famous movements while sharing creative images of how the Mona Lisa may have appeared if painted by other master artists.

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.

The story of a boy and his imaginary friend—told by the imaginary friend Zach should’ve outgrown his imaginary friend by now. He knows this. He’s 11, long past the days when kids are supposed to go on epic make-believe adventures with their invisible friends. But after the death of his father five years ago, all Zach wanted was an escape from the real world. So his imaginary friend, Shovel, hasn’t faded away like the other kids’ have. Their imaginary friendship grew stronger. But now Zach’s in middle school, and things are getting awkward. His best friend ditched him for a cooler crowd. His classmates tease him in the hallways. He still misses his dad. Reality is the worst. Which is why Zach makes regular visits to a fantasy world with Shovel. But is Zach’s overactive imagination helping him deal with loss or just pushing people away? Poignant, humorous, and breathtaking, Imaginary is an inventive story of friendship, loss, and growing up . . . as only an imaginary friend could tell it.

"11 tales you never expected to see!"--Cover.