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 fashion so as 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 a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician. "Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as 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 a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion." "The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician."--Jacket Wapner (mathematics, El Camino College, California) explains to general readers the Banach-Tarski Theorem, or Paradox, which shows how to disassemble a sphere and rearrange the pieces into another solid of any specified shape and volume: thus a pea could be taken apart and reassembled as the sun. He discusses its precursors and history, proof and resolution, and implications for the nature of mathematics and its relation to the physical world. Written 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 an intriguing problem of advanced mathematics accessible to the non-mathematician. . Significant mathematical achievement is best understood when viewed in correct historical and mathematical context. Leonard M. Wapner. Includes Bibliographical References (p. 205-211) And Index.