Synergetic Discovery Between a Pyramid and an Octagon. The featured picture uses octagons. Their synergy parallels the synergetic behavior of the hexagon and tetrahedron. First, to define the terms: Synergy, Pyramid and Octagon. For my reference I quote Buckminster Fuller. His book is Synergetics: Explorations in the Geometry of Thinking.
- Synergy: 101.01 is the “Behavior of whole systems unpredicted by their parts taken separately. “
- Syneretics 108.00- Four Triangles out of Two. Synergy acts on the transformation of the hexagon into a 6-sided tetrahedron. In nature the six sided hexagon (two open ended triangles) synergetically transform into the six-edged tetrahedron.
- Parallel between the square based pyramid and the octagon. A square based pyramid (like the Great Pyramid) has 8 edges. The octagon has 8 edges. The pyramid holds a total of 1080°. The square base has 360 °. Its 4 triangles total 4 x 180° = 720° . The octagon, be it regular or irregular, also has 8 vertices with a total of 1080°.
- Here’s the parallel between my synergetic discovery in #3 with Fuller’s in #2.
As the six edges of 2 open ended triangles become a tetrahedron; Two open-ended squares can become a squared based pyramid. What practical application can this have? Many books have been written about the beneficial effects of the pyramid. These include:
What ever beneficial effects the 3 dimensional pyramid may have, the two dimensional octagon should also have the same effects. As two open ended triangles can converge to form a tetrahedron, two open ended squares can converge to form a pyramid. I have a number of blogs about Buckminster Fuller. Below are a couple of internal links. Geometry can be applied to benefit our daily lives. I think the octagon pyramid parallel is original with myself- Though I am not positive. Feel free to share.