Foreword to Shalosh B. Ekhad XIV's Geometry Textbook

By Doron Zeilberger , the downloader.

One night, very late, I was browsing the internet, using my current computer, Shalosh B. Ekhad, III. I was searching for "Ekhad". All of a sudden, to my amazement, I chanced on a website whose last update was Sept. 30, 2050, and found this little Elementary Geometry textbook.

This text may seem a bit strange to 2001 humans. It appears that there are no proofs, only statements, in Maple, using English-based names for the definitions and theorems. But THE STATEMENT IS THE PROOF, ready to be run on Maple, that will output "true" if the proof-statement is correct, and "false" otherwise. The statement-proofs are collected in the accompanying Maple package RENE.

You don't have to know Maple to savor this book. The names of the commands are English-based, and the primitive definitions like Pt, Le, Ce, etc. are explained in the appropriate links in this completely hyper-texed text.

While this webbook is already a computer program, it must have been automatically generated by another "meta" computer program, as described in the author's Introduction. The output computer program, without the illustrations is RENE (in honor of Rene Descartes). To verify any given theorem, go into Maple, type: read RENE; followed by: TheoremName(); .

The beautiful illustrations were generated by another Maple package PictRENE. It too, must have been generated automatically. With it, you can draw many other diagrams for the theorems, using different input parameters. Once you downloaded PictRENE, get into Maple, type: "read PictRENE:" (without the quotes), and then type "ezra();" (w/o the quotes) to get on-line help.

Cover Introduction Definitions Theorems