Kepler -- Serious Stuff for Discrete Geometers
Serious Stuff for Discrete Geometers
Postscript files of the proof.
There are over 250 pages here in postscript.
The papers can also be obtained from the
xxx archive.
Just click on Hales and Ferguson.
One more paper,
Recent Progress on the Kepler Conjecture,
is not current and is not part of the proof, but it gives
useful background.
Much of the remaining material will be of interest to very few. It
contains all of the computer code and output from various verifications
relating to the Kepler conjecture. It is for the benefit of
those who want to
know the exact details of various verifications.
Linear Programming.
The package cplex was used for
the linear programming. I have links to about 3 gigabytes of cplex-format
linear programming files.
- The crude linear programs
- The batch files, cplex log files, and
Mathematica-format summaries of the cplex sessions of the
crude
linear programs.
- The refined linear programs for
pentagons,
double pentagons,
and
the batch files, cplex log files, and
summaries of the cplex sessions
for pentagons.
A few
cases required extra work. These
are summarized in
log files in a quasi-Mathematica format.
- The refined linear programs for
hexagons and
the batch files, cplex log files, and
summaries of the cplex sessions
for hexagons
A few
cases required extra work. These
are summarized in
log files in a quasi-Mathematica format.
- The refined linear programs for
heptagons and
the batch files, cplex log files, and
summaries of the cplex sessions
for heptagons
- The refined linear programs for
octagons and
the batch files, cplex log files, and
summaries of the cplex sessions
for octagons
There are three files in Mathematica format that generate the cplex-format
linear programming files.
The Mathematica format sed files were created by a
sed program
Planar Maps
The planar maps were generated by a
java program. All the source code is
in that directory, and the archive is contained in a
subdirectory.
The planar
map generation menu is currently disabled in the applet. To
enable this feature of the applet, change the boolean debugMode
to true in the file renderGraph.java and recompile.
A menu will appear in the applet with the options III, quad, pent,
hex, hept, oct. Selecting "quad" will generate all the planar
graphs with at most a quad. The output is sent to the standard output
(the java console). These generate thousands of planar maps and
take a while (several hours) to generate.
Interval arithmetic
This page is available for historical purposes only. It is a copy
from www.math.lsa.umich.edu/~hales/countdown. It has not been
maintained since 1998.