great progress on Conic Section unification with Regular Polyhedra

[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.

When we combine cylinder and cone as the Conic sections we obtain these figures:

circle
oval
ellipse
parabola
hyperbola
parallel line segments (cylinder)
intersecting line segments (two cones)

So we have 7 Cylinder Cone Sections

tetrahedron
cube
octahedron
dodecahedron
icosahedron
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.

AP

[b***@gmail.com]

AP brain farto, more delusional than ever. Trying to
sell his mongo math. The poor guy has definitely

a crytal meth problem, or is it glue sniffing?

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.
circle
oval
ellipse
parabola
hyperbola
parallel line segments (cylinder)
intersecting line segments (two cones)
So we have 7 Cylinder Cone Sections
tetrahedron
cube
octahedron
dodecahedron
icosahedron
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.
AP

[Archimedes Plutonium]

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.
circle
oval
ellipse
parabola
hyperbola
parallel line segments (cylinder)
intersecting line segments (two cones)
So we have 7 Cylinder Cone Sections
tetrahedron
cube
octahedron
dodecahedron
icosahedron
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

AP

[b***@gmail.com]

Nope, oval doesn't need to have an axis:

https://de.wikipedia.org/wiki/Oval#/media/File:Eikuve.svg

The English wiki is wrong, go check the German wiki.

Post by Archimedes Plutonium
oval 1 axis symmetry

[b***@gmail.com]

On the otherhand two symmetry axis are not
a defining property of ellipses.

There are ovals, with two symmetry axis,
that are not ellipses.

Post by b***@gmail.com
https://de.wikipedia.org/wiki/Oval#/media/File:Eikuve.svg
The English wiki is wrong, go check the German wiki.

Post by Archimedes Plutonium
oval 1 axis symmetry

[Archimedes Plutonium]

Post by Archimedes Plutonium
So, the symmetry of the solids
tetrahedron 0 planar symmetry

Let us give it 1

Post by Archimedes Plutonium
parallelepiped 0 planar symmetry

Let us give it 1 as top bottom planar symmetry

Post by Archimedes Plutonium
dodecahedron 1 planar symmetry
pyramid 2 planar symmetry
cube 3 planar symmetry
octahedron 3 planar symmetry
icosahedron 3 planar symmetry

Let us give the icosahedron 1

That leaves them as this

tetrahedron 1
parallelepiped 1
icosahedron 1
dodecahedron 1
pyramid 2
octahedron 3
cube 3

[b***@gmail.com]

With this great progress, I wonder why AP wasn't hired
by Google Street View. They might sure have some tasks

to do for such a great mathematician with so many sills
in geometry, especially the field of mongo math, with its

oval and non-ellipse conic sections. Maybe this will
accelerate the development of self driving cars, thanks

to mongo math, this cars will more quickly find the
next wall to crash into.

Post by Archimedes Plutonium

Post by Archimedes Plutonium
So, the symmetry of the solids
tetrahedron 0 planar symmetry

Let us give it 1

Post by Archimedes Plutonium
parallelepiped 0 planar symmetry

Let us give it 1 as top bottom planar symmetry

Post by Archimedes Plutonium
dodecahedron 1 planar symmetry
pyramid 2 planar symmetry
cube 3 planar symmetry
octahedron 3 planar symmetry
icosahedron 3 planar symmetry

Let us give the icosahedron 1
That leaves them as this
tetrahedron 1
parallelepiped 1
icosahedron 1
dodecahedron 1
pyramid 2
octahedron 3
cube 3

[Jan]

Post by Archimedes Plutonium
With my latest proof on a conic section of oval, never an ellipse,

You have no proof, this is a false claim. Stop daydreaming, man!

--
Jan