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<html><head><title>Experimental Mathematics Website</title>
<LINK REL="SHORTCUT ICON"
href="http://www.experimentalmath.info/favicon.ico">
<meta name="google-site-verification" content="glT1g1IJgm_krdIvbJRra9blEgMtPLUsVykjk4MG4S8" />
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<body BGCOLOR="#FFFFFF">
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<h2>Experimental Mathematics Website<br>
http://www.experimentalmath.info</h2>
<!-- Revised 1 Jan 2026 -->
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in the file "quotes.txt". -->
<h3>
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<a title="Math Scholar blog"
href="https://www.mathscholar.org" target=_blank>Math Scholar blog</a> |
<a title="Math Drudge blog"
href="https://www.experimentalmath.info/blog" target=_blank>Math Drudge blog (older)</a> |
<a title="Math Investor blog"
href="https://www.mathinvestor.org" target=_blank>Math Investor blog</a> |
<a title="Jonathan Borwein site"
href="https://www.jonborwein.org" target=_blank>Jonathan Borwein site</a> |
<a title="Books"
href="http://www.experimentalmath.info/books" target=_blank>Books</a> |
<a title="Commercial sites"
href="http://www.experimentalmath.info/commercial" target=_blank>Commercial sites</a> |
<a title="Institutional sites"
href="http://www.experimentalmath.info/institutional" target=_blank>Institutional sites</a> |
<a title="Non-commercial software and tools"
href="http://www.experimentalmath.info/noncomm" target=_blank>Non-commercial sites</a> |
<a title="Other sites of interest"
href="http://www.experimentalmath.info/othersites" target=_blank>Other sites</a> |
<a title=Software
href="http://www.experimentalmath.info/software" target=_blank>Software</a> |
</DIV>
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mso-cellspacing:3.7pt;border:outset 1.5pt;mso-padding-alt:0in 0in 0in 0in'>
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<p align=center><img width=300 height=300 src=expansion2.png></p>
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<blockquote>
<== This is a picture from the interactive geometry
package <i>Cinderella</i> 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:
<a href="http://users.cs.dal.ca/%7Ejborwein/expansion.html">Expansion</a>
<a href="http://users.cs.dal.ca/%7Ejborwein/reflection.html">Reflection</a>
(wait 30-60 seconds to see the display).
<br><br>
Quote of the day (refresh browser to select another):
<p>
<i> Mathematicians normally think that they possess absolute truth. They read God's thoughts. They have absolute certainty and all the rest of us have doubts. Even the best physics is uncertain, it is tentative. Newtonian science was replaced by relativity theory, and then---wrong!---quantum mechanics showed that relativity theory is incorrect. But mathematicians like to think that mathematics is forever, that it is eternal. Well, there is an element of that. Certainly a mathematical proof gives more certainty than an argument in physics or than experimental evidence, but mathematics is not certain. This is the real message of Godel's famous incompleteness theorem and of Turing's work on uncomputability. </i> -- G. Chaitin, from "The Creative Life: Science vs. Art" <a href="http://www.cs.auckland.ac.nz/~chaitin/cdg.html"> Online article</a>.
<br><br>The complete list of quotes is available
<a href="http://www.experimentalmath.info/quotations.html">here</a>.
</blockquote>
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<p><p>
This website is a repository of information on experimental and computer-assisted mathematics. It is operated by David H. Bailey, Lawrence Berkeley Laboratory (retired)
(<a href="http://www.davidhbailey.com/">DHB website</a>).
Please send any comments or questions for this site to:
<p>
<img border=0 width=200 src=dhb-email.png></p>
<p>
<b>Disclaimer and copyright</b>. 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) 2026.</li>
<p>
<b>Math Scholar blog</b>. 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:
<ul>
<li><a href="https://www.mathscholar.org">https://www.mathscholar.org</a></li>
</ul>
<p>
<b>Math Drudge blog (older)</b>. This blog was co-authored by Bailey and the late Jonathan Borwein, prior to Borwein's death in August 2016.
<ul>
<li><a href="https://www.experimentalmath.info/blog">https://www.experimentalmath.info/blog</a></li>
</ul>
<p>
<b>Jonathan Borwein Memorial site</b>. 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.
<ul>
<li><a href="https://www.jonborwein.org">https://www.jonborwein.org</a></li>
</ul>
<p>
<b>Mathematical Investor blog</b>. The Mathematical Investor blog is devoted to financial mathematics and abuses of mathematics in the field:
<ul>
<li><a href="https://www.mathinvestor.org">https://www.mathinvestor.org</a></li>
</ul>
<h3>Additional information, in alphabetical order:</h3>
<ol>
<li><b>Books</b>. Bailey and Jonathan Borwein (now deceased) have authored numerous books on mathematical and scientific computation. For details on the authors' books on experimental mathematics, see:
<ul>
<li><a href="http://www.experimentalmath.info/books">Book site</a></li>
</ul>
<br>
<li><b>Commercial sites</b>. For a list of websites of numerous commercial firms that offer mathematical software and (free) online tools, see the Commercial site page:
<ul>
<li><a href="http://www.experimentalmath.info/commercial">Commercial sites</a></li>
</ul></li>
<br>
<li><b>Institutional sites</b>. For a list of websites of mathematical societies and journals in the general area of experimental and computational mathematics, see the Institutional site page:
<ul>
<li><a href="http://www.experimentalmath.info/institutional">Institutional sites</a></li>
</ul>
<br>
<li><b>Non-commercial software and tools</b>. For a list of websites of non-commercial organizations that offer mathematical software and (free) online tools, see the Non-commercial site page:
<ul>
<li><a href="http://www.experimentalmath.info/noncomm">Non-commercial sites</a></li>
</ul>
<br>
<li><b>Other sites of interest</b>. For a list of numerous other websites with interesting and useful information relevant to mathematics in general and computational mathematics in particular, see the Other site page:
<ul>
<li><a href="http://www.experimentalmath.info/othersites">Other sites</a></li>
</ul></li>
<br>
<li><b>Software</b>. For some freely downloadable software for experimental math research, see the Software page:
<ul>
<li><a href="http://www.experimentalmath.info/software">Software</a></li>
</ul></li>
<ol>
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