On Friday, August 18, 2023 at 2:13:22 AM UTC-5, Archimedes Plutonium wrote:
There is a picture of this uniqueness in Quanta-magazine, 2020 "Mathematicians Report New Discovery About the Dodecahedron"
"Suppose you stand at one of the corners of a Platonic solid. Is there some straight path you could take that would eventually return you to your starting point without passing through any of the other corners?"
Apparently of the 5 Platonic Solids, only the Dodecahedron has this feature.
Now, how am I to translate that feature into Quantum Physics Electrodynamics?
I am holding a dodecahedron in my hands now, and see that each face has a opposite face but the pentagon is upside down. Is it a parallel plate capacitor and the corner would be like a Dirac magnetic monopole as a straight line closed loop circuit.
The article says the cube does not have this feature. For I would have thought the cube was the geometry to represent parallel plate capacitor. Instead, the Dodecahedron is better.
Now I am going to argue against the three mathematicians Jayadev Athreya, David Aulicino, Patrick Hooper who claim only the dodecahedron has this property, and none of the other 4 of 5 regular polyhedra. The cube is a regular polyhedra, and therectangular solid, although not a regular polyhedra is much and the same like a cube.
If we admit the rectangular solid along with the 5 regular polyhedra, we then have 2 solids with this property and not just the dodecahedron alone.
AP
Drs.Jayadev Athreya, David Aulicino, Patrick Hooper may have been victims of Computer Graphing rather than realized fundamental truths of geometry. This happened to me also with the case of tiling a sphere, that the computer gives a image as though thesphere was tiled by hexagons. And computers can make a picture that is so much con-art and deceiving of the human eyes, like optical illusions.
When I first saw this graphics by Jayadev Athreya, David Aulicino, Patrick Hooper, I thought to myself that the "straight line they spoke of cut the Dodecahedron in 1/2". Much like a sphere circumference splits the sphere into two equal semisphere,whereas a cut that does not yield two semispheres, although a circle, would not be considered a "line in sphere surface geometry".
So I suspect, and it must be checked thoroughly whether Jayadev Athreya, David Aulicino, Patrick Hooper are deluded about their dodecahedron, deluded from images of Computer Graphics than real true geometry. And they certainly would not be the first tobe deluded by computer graphics, and AP's request to throw out all research in geometry that is based in part on Computer graphics.
So, well, I ask Drs. Jayadev Athreya, David Aulicino, Patrick Hooper, when they speak of "straight line across the Dodecahedron" what exactly do they mean??? Do they mean it splits the Dodecahedron in half???? For I have my plastic Rectangular Box, andit qualifies for the same special characteristic traits of uniqueness that the Dodecahedron is given by Drs. Jayadev Athreya, David Aulicino, Patrick Hooper.
There is a picture of this uniqueness in Quanta-magazine, 2020 "Mathematicians Report New Discovery About the Dodecahedron"sphere was tiled by hexagons. And computers can make a picture that is so much con-art and deceiving of the human eyes, like optical illusions.
"Suppose you stand at one of the corners of a Platonic solid. Is there some straight path you could take that would eventually return you to your starting point without passing through any of the other corners?"
Drs.Jayadev Athreya, David Aulicino, Patrick Hooper may have been victims of Computer Graphing rather than realized fundamental truths of geometry. This happened to me also with the case of tiling a sphere, that the computer gives a image as though the
Alright it looks to me that Quanta-magazine is partly anti-science and anti-math as to publish rubbish of a Dodecahedron.a cut like a conic section.
Looking at the picture they include a region of the vertex-- is it 1mm from the vertex point?? Is it 1.5mm, is it 2mm. Then they provide no definition of "straightline path", can it vary in direction every face of the dodecahedron, or is it meant to be
The only figure on my desk that qualifies as cutting the figure in half and a path returns to vertex is the Pyramid of its apex vertex, and only its apex vertex.error filled math, is anti-math.
I deem this article as math rubbish, that deceives more than elucidates geometry.
Since when is a vertex a *region of vertex*? What is a straightline path if not a murky and obfuscation?
Perhaps the only lesson to learn from this anti-math of dodecahedron, is that the Computer Graphics destroys the truth of geometry and all geometry proofs starting with Appel & Haken 4 Color Mapping to Hales's claim of Kepler Packing is flawed and
Every geometry entry into mathematics is bogus math, because a computer has no biological mind to see into Space. A computer prints out what the person wants to see and hear and not the reality of the world of geometry.
In geometry and proofs of geometry, no computer should step foot into.
On Friday, August 18, 2023 at 11:27:41 PM UTC-5, Archimedes Plutonium wrote:triangular planes. I cannot retrieve a pentagon plane nor a hexagon plane. And proofs should be provided.
Is the 4 sided plane the largest plane in terms of sides for the 3D 10 Grid? At the moment, I cannot envision nor picture any plane with 5 sides or 6 or more. I suspect 4 is the maximum.
The shape of 3D 10 Grid is a cube shape, so I am asking if there is a cross section of the inside of a cube that yields a 5 or higher sided figure? None that I can see, for the 6 faces of the cube only allow 4 sided 2D figures to emerge or 3 sided
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