Magnificent Mistakes in Mathematics 

Author:
 Posamentier, Alfred S. Lehmann, Ingmar 
ISBN:  9781616147471 
Publication Date:  Aug 2013 
Publisher:  Prometheus Books, Publishers

Book Format:  Hardback 
List Price:  USD $24.00 
Book Description:

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 D#65533;couverte in Paris. However, in...
More Description 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 D#65533;couverte 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 timehonored 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 highschoollevel math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, allimportant science.