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 <== This is a picture from the interactive geometry package Cinderella showing the behavior of 10,000 starting values in the rectangle [0,1]x[h-1,h+1], where h is the height of the horizontal line, after six iterations of the algorithm which reflects a point x in the sphere then reflects the outcome in the line and then averages the result y with x. It is an accessible prototype for a remarkable image reconstruction algorithm known variously as Douglas-Ratchford, Lion-Mercier, Fienup's method, and "divide-and-concur." Some related graphics can be generated and displayed at these URLs: Expansion Reflection (wait 30-60 seconds to see the display). Quote of the day (refresh browser to select another): When I was a young student in the United States, I met Zygmund and I had an idea how to produce some very complicated functions for a counter-example and Zygmund encouraged me very much to do so. I was thinking about it for about 15 years on and off, on how to make these counter-examples work and the interesting thing that happened was that I realised why there should be a counter-example and how you should produce it. I thought I really understood what was the background and then to my amazement I could prove that this "correct" counter-example couldn't exist and I suddenly realised that what you should try to do was the opposite, you should try to prove what was not fashionable, namely to prove convergence. The most important aspect in solving a mathematical problem is the conviction of what is the true result. Then it took 2 or 3 years using the techniques that had been developed during the past 20 years or so. -- Lennart Carleson, 1966, from 1966 IMU address on his proof of Luzin's 1913 conjecture that the Fourier series of every square integrable function converges a.e. to the function. The complete list of quotes is available here.

This website is a repository of information on experimental and computer-assisted mathematics. It is operated by David H. Bailey, Lawrence Berkeley Laboratory (retired), and University of California, Davis (DHB website). Please send any comments or questions for this site to:

Disclaimer and copyright. Material on this site is provided for research purposes only and does not necessarily reflect the views or policies of the author's institutions or any other organization. Except where explicitly stated otherwise, all material is copyrighted by David H. Bailey (c) 2022.

Math Scholar blog. The "Math Scholar" blog contains essays, philosophical musings, interesting quotes and exercises, all in the realm of mathematics, computing and modern science. New items are posted on average every two weeks:

Math Drudge blog (older). This blog was co-authored by Bailey and the late Jonathan Borwein, prior to Borwein's death in August 2016.

Jonathan Borwein Memorial site. In the wake of Jonathan Borwein's untimely death in August 2016, this site contains a blog of remembrances of Jon by family, friends and colleagues, together with a compendium of Jon's publications, talks and reviews of his work by others.

Mathematical Investor blog. The Mathematical Investor blog is devoted to financial mathematics and abuses of mathematics in the field: