Steve Curtis is a mathematics teacher at the Curtis School. He is also a football coach (defensive backs).
This project officially began on December 19, 2011 in Steve’s classroom with his three geometry classes and two ACT preparation classes. The class learned about base-2 exponential notation by observing nested geometries using the tetrahedron and octahedron.
The process. These classes went deeper and deeper inside each object by dividing each edge in half and by connecting the new vertices to create a smaller set of nesting tetrahedrons and octahedrons. By about the 45th step within — on paper — the size of the tetrahedron and octahedron was about the size of a fermion. Within about 67 more steps, that size was approaching the Planck Length. At that time there were about 112 steps within from the size of our original plastic models.
We then went out into the universe by multiplying each edge by 2. Somewhere between 90 and 98 steps, we were in the area of the Observable Universe. It wasn’t until we followed Planck Time to the Age of the Universe did we finally settle on just over a total of 202 notations.
This project has been under the watchful eye of Steve Curtis right from its beginning.
Tilings and Tessellations from Cambridge, England
A tessellation is the tiling of a plane using geometric shapes called tiles and it has no gaps or overlaps.
In our search of the web for images of tetrahedrons and tessellations or tilings of triangles, squares and hexagons, there were thousands of possibilities. Among the best were these very clean images from Jo Edkins, especially made for teachers.
Jo is from the original Cambridge in England and loves geometry. She has encouraged us in our work and, of course, we thank her and her family’s wonderful creativity and generosity of spirit.
The Edkins triangular tessellations
Jo’s square tessellations
For more variations, go to Jo’s website: http://gwydir.demon.co.uk/jo/tess/grids.htm
The text within the picture reads as follows:
Three levels of simple complexity:
1. Observe the tetrahedron in the bottom left corner.
2. Notice that it is enclosed in a larger tetrahedron. Right beside is
an octahedron, plus there is a tetrahedron in each of the other three corners. Every tetrahedron encloses four half-sized tetrahedrons and an octahedron.
3. Notice that our larger tetrahedron is enclosed by an even larger tetrahedron. This pattern repeats itself getting smaller and getting larger. Part of the complexity can be seen by observing the center octahedron. Notice the red, black and blue hexagonal plates. A white plate has been obscured.
For more, please follow this page on the website:
“Tiling the Universe in 201+ Exponential Notations:
The Great Chain of Being”