The Pea and the Sun: A Mathematical Paradox

Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a manner that would to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the Sun by breaking something so small as a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Wapner writes in an engaging style that catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox, making one of the most intriguing problems of advanced mathematics accessible to the non- math-ematician.

Leonard M. Wapner is Professor of Mathematics at El Camino College in Torrance, CA. He received his BA and MAT degrees in mathematics from the University of California, Los Angeles. During his thirty-year tenure at El Camino, his writings on mathematics education have appeared in The Mathematics Teacher and The AMATYC Review.