Magnificent Mistakes in Mathematics

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. Veteran math educators Alfred S. Posamentier and Ingmar Lehmann demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts. For example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even