PODCAST · science
The Geometry of Closed Packed Spheres
by Nick Trif
The Geometry of Closed Packed SpheresMission statement: To change minds, to open eyes, to educate and inspire people designing and building better worlds.Beauty makes beautiful things beautiful!A sphere can be completely surrounded by exactly twelve other identical spheres. Close-packing of spheres helps us explore the shape of the physical space. A good design of a 3D structure shall obey the principles, freedom, and constraints imposed by the physical space around us.
Episodes
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18. The Square Roots Spiral
The document explores the concept of incommensurability in mathematics, focusing on the relationship between numbers and their square roots. It introduces the square roots spiral as a visual representation of incommensurable magnitudes. The text then contrasts the square roots spiral with two…
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17. Lines Patterns in Space
The text discusses the concept of straight lines in CPS Geometry, a system where points are infinitesimal spheres arranged in a specific pattern. It explores the concept of lines as patterns that extend infinitely in both directions and can be defined by any two points in the space. The text then...
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16. The Fibonacci Sequence
The source explains the connection between the Fibonacci sequence and the Golden Ratio, also known as the Golden Section. The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding numbers (e.g., 1, 1, 2, 3, 5, 8). The Golden Ratio is an irrational number,...
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15. The Golden Section
The text explores the Golden Ratio, also known as the Golden Section, and its significance in classical geometry. It highlights three primary ways the Golden Ratio manifests itself: through Euclid's definition of dividing a line into extreme and mean ratio, in the construction of a regular...
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14. Similarity Theorem in CPS Geometry
The source explores the concept of similarity in geometry, arguing that traditional Euclidean geometry’s reliance on the parallel postulate is not the most fundamental approach. Instead, the source proposes a "CPS Geometry" based on the close-packing of spheres, where similarity arises from the...
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13. Archimedean Solids
The text describes the 13 Archimedean solids in terms of their relationship to the close-packing of spheres (CPS) arrangement. The author explains how these semi-regular polyhedrons, such as the cuboctahedron, truncated tetrahedron, and truncated icosahedron, can be constructed by manipulating...
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12. The Rhombic Dodecahedron in CPS
This excerpt from "12-The Rhombic Dodecahedron in CPS.pdf" explores the presence of the rhombic dodecahedron in the Close Packing of Spheres (CPS) model. It argues that the shape of the rhombic dodecahedron, a space-filling form, emerges from a multitude of spheres arranged in a specific pattern....
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11. Platonic Solids in CPS Geometry
This source discusses the five Platonic solids, or perfect bodies: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The author argues that these solids are not mystical, but rather can be explained using the principle of close-packing of spheres in a specific arrangement called…
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10. Close Packing of Spheres
The text explains the concept of close packing of spheres, a principle that describes how spheres can be arranged in three-dimensional space to achieve the densest possible packing. It highlights the two primary lattice patterns used in this arrangement: the square lattice and the hexagonal...
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09. CPS Geometry
The provided text introduces Closed Packed Spheres (CPS) Geometry, an alternative geometric system that challenges traditional Euclidean geometry. Unlike Euclidean geometry, which defines points as dimensionless and structureless, CPS Geometry views points as infinitesimally small, identical...
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08. The Mental-Experimental Method
The source criticizes the axiomatic method of Euclidean geometry, arguing that it stifles creativity and prevents discovery by imposing a rigid, bureaucratic system. It proposes instead a "Mental-Experimental Method" that relies on mental visualization and experimentation to understand geometric...
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07. The Dialectic Process
The text draws a parallel between the incommensurability of the square root of two and the distribution of prime numbers, arguing that neither can be fully understood or expressed using simple patterns. The author then references Plato's dialectic method, which utilizes a series of hypotheses to...
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06. The Incommensurables – Arithmetical Proof
The provided text explores the concept of incommensurability, specifically focusing on the square root of 2. The text outlines two methods for understanding incommensurability: a geometric approach that is intuitive but potentially less rigorous, and an arithmetical approach that uses logic and...
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05. The Incommensurables – Geometrical Proof
The text discusses the discovery of incommensurable magnitudes, a fundamental concept in mathematics. This discovery, made by the Pythagoreans, demonstrated that not all line segments can be measured using a common unit of length. The text uses the example of a square's diagonal and its side to...
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04. The Euclidian Algorithm
Chapter 4 of the book: “From Riemann Hypothesis to CPS Geometry and Back Volume 1 (https://www.amazon.com/dp/B08JG1DLCV) ”, Canadian Intellectual Property Office Registration Number: 1173734...
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03. Gauss Estimation An Epistemological Problem
Chapter 3 of the book: “From Riemann Hypothesis to CPS Geometry and Back Volume 1 (https://www.amazon.com/dp/B08JG1DLCV) ”, Canadian Intellectual Property Office Registration Number: 1173734...
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03 (Old). Gauss’s Estimation – An Epistemological Problem
Chapter 3 of the book: “From Riemann Hypothesis to CPS Geometry and Back Volume 1 (https://www.amazon.com/dp/B08JG1DLCV) ”, Canadian Intellectual Property Office Registration Number: 1173734...
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02. A Perfect Experiment
Chapter 2 of the book: “From Riemann Hypothesis to CPS Geometry and Back Volume 1 (https://www.amazon.com/dp/B08JG1DLCV) ”, Canadian Intellectual Property Office Registration Number: 1173734...
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01. The Scientific Method
Chapter 1 of the book: “From Riemann Hypothesis to CPS Geometry and Back Volume 1”, Canadian Intellectual Property Office Registration Number: 1173734, Ottawa, ISBN 9798685065292, 2020. On Google Books: https://books.google.ca/books/about?id=jFQjEQAAQBAJ&redir_esc=y On Google Play:...
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Preface to CPS Geometry Book
Book: Amazon.com: From Riemann Hypothesis to CPS Geometry and Back: Volume 1 eBook : Trif, Nick: Kindle Store On Google Books: https://books.google.ca/books/about?id=jFQjEQAAQBAJ&redir_esc=y This text introduces the concept of "Closed Packed Singularity Geometry" (CPS Geometry), a new geometric...
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Determining a location within a physical structure
US Patent: https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/9245059 A system and method for determining a location within a physical structure are described. The location within the physical structure can be determined by storing a model of a physical structure comprising a...
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The Ratio of the Mass of the Proton and the Mass of the Electron
The ration of the most precise measurements of the mass of the proton and the mass of the electron is very closed to 694 multiplied by square root of 7. See: https://www.amazon.com/dp/B09RJNMZPV
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Closed Packed Spheres - Overview
The Geometry of Closed Packed Spheres Mission statement: To change minds, to open eyes, to educate and inspire people designing and building better worlds. Beauty makes beautiful things beautiful! A sphere can be completely surrounded by exactly twelve other identical spheres. Close-packing of...
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ABOUT THIS SHOW
The Geometry of Closed Packed SpheresMission statement: To change minds, to open eyes, to educate and inspire people designing and building better worlds.Beauty makes beautiful things beautiful!A sphere can be completely surrounded by exactly twelve other identical spheres. Close-packing of spheres helps us explore the shape of the physical space. A good design of a 3D structure shall obey the principles, freedom, and constraints imposed by the physical space around us.
HOSTED BY
Nick Trif
CATEGORIES
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How many episodes does The Geometry of Closed Packed Spheres have?
The Geometry of Closed Packed Spheres currently has 23 episodes available on PodParley. New episodes are automatically indexed when they're published to the podcast feed.
What is The Geometry of Closed Packed Spheres about?
The Geometry of Closed Packed SpheresMission statement: To change minds, to open eyes, to educate and inspire people designing and building better worlds.Beauty makes beautiful things beautiful!A sphere can be completely surrounded by exactly twelve other identical spheres. Close-packing of spheres...
How often does The Geometry of Closed Packed Spheres release new episodes?
The Geometry of Closed Packed Spheres has 23 episodes. Check the episode list to see recent publication dates and frequency.
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Who hosts The Geometry of Closed Packed Spheres?
The Geometry of Closed Packed Spheres is created and hosted by Nick Trif.
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