List journal issues    
 
 
Home List journal issues Table of contents Subscribe to APQ

Article

Volume 50 • Number 1

January 2013



 

 

To Let: Unsuccessful Stipulation, Bad Proof, and Paradox


by Laurence Goldstein


Letting is a common practice in mathematics. For example, we let x be the sum of the first n integers and, after a short proof, conclude that x = n(n+1)/2; we let J be the point where the bisectors of two of the angles of a triangle intersect and prove that this coincides with H, the point at which another pair of bisectors of the angles of that triangle intersect. Karl Weierstrass's colleagues, in an attempt to solve optimization problems, stipulated that the minimum area for a triangle with a given perimeter be a straight line segment conceived as a triangle with zero altitude. (Weierstrass complained that this obscured the insight that some problems have no solutions.) In mathematics applied to physics, we let x be the temperature in Fahrenheit corresponding to 30° Centigrade; we let v be the velocity of the Earth through the luminiferous ether. Before the error was spotted, the official rules for Little League Baseball made an inconsistent stipulation about the dimensions of home plate (Bradley 1996).


view PDF
 

 

 

 
Home | Issue Index
 
© 2012 by the Board of Trustees of the University of Illinois
Content in American Philosophical Quarterly is intended for personal, noncommercial use only. You may not reproduce, publish, distribute, transmit, participate in the transfer or sale of, modify, create derivative works from, display, or in any way exploit the American Philosophical Quarterly database in whole or in part without the written permission of the copyright holder.

American Philosophical Quarterly is published by the University of Illinois Press on behalf of North American Philosophical Publications.

ISSN: 2152-1123