Electronic Proceedings of the Eighteenth Annual International Conference on Technology in Collegiate MathematicsOrlando, Florida, March 1619, 2006Paper C037
This is an electronic reprint, reproduced by permission of Pearson Education Inc. Originally appeared in the Proceedings of the Eighteenth Annual International Conference on Technology in Collegiate Mathematics, Edited by Joanne Foster, ISBN 0321491602, Copyright (C) 2007 by Pearson Education, Inc. 
Finding the Brachistochrone Between Two Points in a Vertical Plane by Direct Numerical Integration 
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In 1696, Bernoulli proposed determining the 'curve of quickest descent' between two points in a vertical plane. As is well known, the solution involves finding a function to make an integral an extreme. Here we verify this by numerically calculating the transit time between two points joined by various curves.
Keyword(s): numerical methods, calculus