The Geometry of Closed Packed Spheres

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 root

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

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 wh

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 manife

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 ap

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

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 t

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 a

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 possib

09. CPS Geometry

The provided text introduces Closed Packed Spheres (CPS) Geometry, an alternative geometric system that challenges traditional Euclidean geometry. Unlike Euclidean geomet

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 p

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

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 incommensurab

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

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 Registr

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 Registr

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 Registr

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 Regist

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 979

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=jF