PlatonicStructures

Black Shadow Moving Across the Sky April 04, 2023 - Aylmer, Quebec, Canada

Menelaus Theorem in CPS Geometry

Sun Rise - Punta Cana - March 2023

Pink Lake - Gatineau Park Quebec Canada October 2022

The ratio between the mass of the proton and the mass of the electron can be expressed as: Mass of Proton = (694 * square root of 7)* Mass of the Electron Is this just a coincidence? This is the first Part of a short series of video investigation this finding. Beauty makes beautiful thing beautiful! Enjoy.

In a plane, spheres can be arranged in a plane in such a way that each ball touches exactly six other balls. This is the hexagonal lattice. In this case, the planes are closer packed than in the square arrangement. But a ball placed in a nest formed by a cluster of three balls does not sink as deep as a ball placed in a nest of a cluster formed by four balls - as we have seen in the square arrangement. As seen previously in the square arrangement, again each ball in the hexagonal arrangement also has exactly twelve neighbors in space. In this there are three balls in the plane below, six balls in the same plane and three balls in the plane above.

In a plane, spheres can be arranged in a plane in such a way that each ball touches exactly four other balls. This is the square lattice. The plane above and the plane below follow the same pattern. The spheres from the second plane fit perfectly in the nests form by four spheres from the first plane. The square pattern is seen better when using struts to connect the nodes.

A sphere can be completely surrounded by exactly twelve others identical spheres. By connecting the spheres with struts, along the directions imposed by close packing of spheres pattern, one ends up with Platonic Structures.

Force Addition and Subtraction - Problem 10 - Resolution of a Force

Physical Phenomena - Problem 10 - Magnetic Phenomena

Physical Phenomena - Problem 07 - Electric Phenomena

Physical Quantities - Problem 06 - Units of Length and Surface

Measurements and Units - Length Measurement - Problem 01

Step by step visualization for building the shell for a Dodecahedron structures from identical spheres packed in a close packing arrangement.

Close Packing of Spheres and the logical structure of the physical space. The points are infinitesimal spheres in a close packing arrangements. They create the physical space. For more information see: http://www.platonicstructures.com Beauty makes beautiful things beautiful!

Pell's Equation and its importance in CPS Geometry: 1. Approximating Square Roots 2. Triangular-Square Numbers 3. Generating Solutions - Brahmagupta’s Identity 4. Finding the Fundamental Solution – The Seed 5. Hand’s On - Example

Visualization of the Gaussian plane. The concept of Gaussian primes, and other related concepts, can be extended to all CPS Planes.

The Gaussian plane is just the simplest CPS Plane. The concept of Gaussian primes, and other related concepts, can be extended to all CPS Planes.

37. CPS Geometry - Brahmagupta's Identity - Planes in Space - Part 3 We continue the connection between the distributions of CPS points on the CPS Planes using the Brahmagupta’s Identity. The CPS nodes, belonging to these planes are closed under multiplication.

36. CPS Geometry - Brahmagupta–Fibonacci Identity - Planes in Space - Part 2 A connection is made between the distribution of CPS points on the simplest CPS Plane and the Brahmagupta–Fibonacci Identity. Both, the magnitude of a number and the two terms of the square sum decomposition are needed to uniquely localize a CPS point in plane. The CPS nodes, belonging to this plane are closed under multiplication.

Now is time, to move to the next critical concept of the CPS Geometry, The Plane, or better said the CPS Plane. Arguably, the plane is the most important concept of any geometry, including the CPS Geometry. In part one we will look at the simplest plane found in the CPS space and identified some of its properties.

The analytical geometry, introduced by Descartes, has changed the direction, the interpretation and the understanding of math and science in a very fundamental and dramatic way. By associating an orthogonal coordinate system of axes to the Euclidean plane, the geometrical point is reduced to an order pair of numbers. These days, without any understanding or logical justification, the Cartesian methods are applied with no restriction to almost everything.

The Proof for Riemann Hypothesis? - Part 2 The number of points located at a given distance from a center point can be only: 6, 24 and 48. For a tutorial see: http://www.platonicstructures.com/TutorialIndex.html For more information see: http://www.platonicstructures.com Beauty makes beautiful things beautiful!