Post by Archimedes Plutonium
With my latest proof on a conic section of oval, never an ellipse, and where the ellipse is a cylinder section, breathes new life in my unification program. Because the linchpin for the proof is to note the axes of symmetry.
So we have now a concept to work with for unification. Axes of symmetry in 2 Dimension and Planes of Symmetry in 3rd Dimension.
parallel line segments (cylinder)
intersecting line segments (two cones)
So we have 7 Cylinder Cone Sections
rectangular solid (maybe parallelopiped)
two pyramids (from octahedron)
both have 7 categories.
Now let me sort them out as to degrees of symmetry. They have to match for a unification.
Some signals already are suggestive of correctness. The two line segments from 2 cones and the 2 pyramids from octahedron.
So, I have been waiting all this time to find the proper concept that links both groups together, and apparently it is symmetry.
So I promised not to start the next edition of Correcting Math, until I was well under way of solving this unification. Today it seems I come much closer.
So the unifying concept parameter is degree of Symmetry.
In 2nd dimension it would be axis of symmetry, left-right, up-down
In 3rd dimension it would be planar symmetry of xy, yz, xz
So, the symmetry of the solids
tetrahedron 0 planar symmetry
parallelepiped 0 planar symmetry
dodecahedron 1 planar symmetry
pyramid 2 planar symmetry
cube 3 planar symmetry
octahedron 3 planar symmetry
icosahedron 3 planar symmetry
two parallel lines 0 axes symmetry
two intersecting lines, 0 axes of symmetry
oval 1 axis symmetry
parabola 1 axis symmetry
hyperbola 2 axes symmetry
ellipse 2 axes symmetry
circle 2 axes symmetry
So, the numbers are not congruous, and need more work