9-12 Geometry Class STEM Tool Excites, But Puzzles Us.

National Council of Teachers of Mathematics

NCTM is the world’s largest mathematics education organization
1906 Association Drive, Reston, Virginia 20191

First email: September 10, 2020, 6:02 PM 

RE: Mathematically mapping the universe
Yes, even our best 6th graders appreciated this STEM tool!

Hi –

Homegrown STEM tools can be inspirational and ours was no exception.  In our geometry classes we divided the edges of a tetrahedron in half and discovered the four smaller tetrahedrons in each corner and an octahedron in the middle. We then divided the edges of that octahedron in half and found the smaller octahedrons in the six corners and eight tetrahedrons, one in each face. Thinking a bit like Zeno, we continued the process of dividing by 2. In 45 steps (on paper only), we were in the area of the CERN-scale of particles and waves and in 67 more steps going within, we were within the Planck scale. We then used the Planck Length and Planck Time, multiplied by 2, and in 112 steps we were back out to the classroom’s original objects but we were at a fraction of a fraction of a second. In just another 90 steps or doublings, we were out to the Age of the Universe and the Observable Universe.

Just 202 doublings. We wondered about our simple logic. Did we just mathematically include everything, everywhere for all time?

It was much more granular than Kees Boekes 1957 work using base-10 to chart the universe in 40 jumps. Ours was based on Planck base units and it had a de facto geometry.

We dubbed our model “the perfect STEM tool.” Even our AP sixth grade science class understood it! But, when we sent our little STEM project to Scientific American, they ignored us. Even Wikipedia rejected our summary as “original research.” The AAAS and Nature magazines rejected us without comment. We’ve written to a diversity of scholars and even they are reluctant to comment.

So, we’re going back over our logic and math, asking, “What are we doing wrong?

Perhaps there is someone out there who could help us?

Thank you.

Most sincerely,


PS. The original letter to the AAAS was signed by the head of our math department, one of our best students, our physics teacher, and me. -BEC

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