Formally named in 2023 by Eric Weisstein, Wolfram MathWorld

Introduction. In 2023 in a note to Eric Weisstein of Wolfram MathWorld, I asked if the five-tetrahedral and five-octahedral gaps had a formal name. Of course, Stephen Wolfram’s Mathematica has become a major part of mathematical computation and Wolfram’s MathWorld has become an encyclopedia and computational resource for schools around the world. One of the key contributors to this encyclopedia is MathWorld’s founder, Dr. Eric Weisstein. He named the gap! And rather quickly, it has been indexed by the web’s search engines. That’s history in the making!

The five-tetrahedral gap has a name! And, we will propose to Eric that every 7.35610… degree gap could now be known as an Aristotle gap, all while reminding us that even the greatest minds among us make mistakes. Aristotle wrote that we could tile and tessellate the universe with a tetrahedron became popular belief for 1800 years before being corrected.

If goes to show that we are all fallible.

Among those geometers who have studied this gap, I remember at least one scholar suggested that this gap is a dimensionless constant. I’ll re-discover that reference and place it here and within several other pages on this site.

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