Circles Squares And Other Beasts

This story begins with a square town. A little round lady moves into town. Then an unusual beast wanders by and decides to stay. Can they all work together to make Block Town a better place?

The itinerant Neoplatonic scholar Giordano Bruno (1548–1600), one of the most fascinating figures of the Renaissance, was burned at the stake for heresy by the Inquisition in Rome on Ash Wednesday in 1600. The primary evidence against him was the book Spaccio de la bestia trionfante, a daring indictment of the church that abounded in references to classical Greek mythology, Egyptian religion (especially the worship of Isis), Hermeticism, magic, and astrology. The author of more than sixty works on mathematics, science, ethics, philosophy, metaphysics, the art of memory, and esoteric mysticism, Bruno had a profound impact on Western thought.

Humanity's love affair with mathematics and mysticism reached a critical juncture, legend has it, on the back of a turtle in ancient China. As Clifford Pickover briefly recounts in this enthralling book, the most comprehensive in decades on magic squares, Emperor Yu was supposedly strolling along the Yellow River one day around 2200 B.C. when he spotted the creature: its shell had a series of dots within squares. To Yu's amazement, each row of squares contained fifteen dots, as did the columns and diagonals. When he added any two cells opposite along a line through the center square, like 2 and 8, he always arrived at 10. The turtle, unwitting inspirer of the ''Yu'' square, went on to a life of courtly comfort and fame. Pickover explains why Chinese emperors, Babylonian astrologer-priests, prehistoric cave people in France, and ancient Mayans of the Yucatan were convinced that magic squares--arrays filled with numbers or letters in certain arrangements--held the secret of the universe. Since the dawn of civilization, he writes, humans have invoked such patterns to ward off evil and bring good fortune. Yet who would have guessed that in the twenty-first century, mathematicians would be studying magic squares so immense and in so many dimensions that the objects defy ordinary human contemplation and visualization? Readers are treated to a colorful history of magic squares and similar structures, their construction, and classification along with a remarkable variety of newly discovered objects ranging from ornate inlaid magic cubes to hypercubes. Illustrated examples occur throughout, with some patterns from the author's own experiments. The tesseracts, circles, spheres, and stars that he presents perfectly convey the age-old devotion of the math-minded to this Zenlike quest. Number lovers, puzzle aficionados, and math enthusiasts will treasure this rich and lively encyclopedia of one of the few areas of mathematics where the contributions of even nonspecialists count.

The Aegysians and the Beast Men have been at war for generations until Aram, brother of the Beast King, is captured. Helped to escape by the enemy king's daughter, Senset, Aram’s praise of her prompts the Beast Men’s leader to seek peace with his enemy. Michael of Habiru is under a curse from God that can be broken only by someone with unselfish love. Believing Senset is that person, he asks for her hand in marriage as part of the peace treaty. Though Senset has doubts, she agrees because it will bring peace for their kingdoms. Can two people making decisions for the wrong reasons bring about change for both their lives and for the future of their kingdoms forever?