The genesis of this article was a simple question: ``How can one use the computer in dealing with computationally approachable but otherwise intractable problems in mathematics?'' We began our current exploration of experimental mathematics by examining a number of very long--standing conjectures and strongly held beliefs regarding decimal and continued fraction expansions of certain elementary constants. These questions are uniformly considered to be hopelessly intractable given present mathematical technology. Unified field theory or cancer's ``magic bullet'' seem accessible by comparison. But like many of the most tantalizing problems in mathematics their statements are beguilingly simple. Since our experimental approach was unlikely to result in any new discoveriesgif, we focused on two aspects of experimentation: systematization and communication.
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