The Geometry of Closed Packed Spheres

By Nick Trif

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!

... more

Download on the App Store

Download on the App Store

Get it on Google Play

FAQs about The Geometry of Closed Packed Spheres:

How many episodes does The Geometry of Closed Packed Spheres have?

The podcast currently has 23 episodes available.

The Geometry of Closed Packed Spheres episodes:

October 01, 2024 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 principles. The author advocates for a more intuitive and experiential approach to geometry, exemplified by their development of CPS Geometry, which emphasizes hands-on exploration and the tangible observation of geometric patterns and relationships.
...more
6min
September 30, 2024 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 reach a higher understanding of knowledge. This method is seen as analogous to the process of reasoning about the distribution of primes, suggesting that it requires a multi-layered approach to fully comprehend its complexity.
...more
7min
September 28, 2024 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 number theory to provide a more formal proof. The arithmetical approach is illustrated by the proof by contradiction, which demonstrates that the square root of 2 cannot be expressed as a ratio of two integers. The text argues that despite the emphasis on the arithmetical approach in modern mathematics, there is value in exploring the potential for combining geometric and arithmetical methods to gain deeper insights.
...more
5min
September 27, 2024 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 illustrate this concept. The process of repeatedly trying to find a common unit of length between the diagonal and side of the square reveals that this task is impossible, as the process continues indefinitely. This led to the creation of irrational numbers, a new category of numbers that cannot be expressed as fractions of integers. This discovery had a profound impact on the development of mathematics, expanding the understanding of numbers and their relationship to geometry.
...more
4min
September 26, 2024 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 (http://www.ic.gc.ca/app/opic-cipo/cpyrghts/srch.do?lang=eng&page=1&searchCriteriaBean.textField1=1173734&searchCriteriaBean.column1=COP_REG_NUM&submitButton=Search&searchCriteriaBean.andOr1=and&searchCriteriaBean.textField2=&searchCriteriaBean.column2=TITLE&searchCriteriaBean.andOr2=and&searchCriteriaBean.textField3=&searchCriteriaBean.column3=TITLE&searchCriteriaBean.type=&searchCriteriaBean.dateStart=&searchCriteriaBean.dateEnd=&searchCriteriaBean.sortSpec=&searchCriteriaBean.maxDocCount=200&searchCriteriaBean.docsPerPage=10) , Ottawa, ISBN 9798685065292, 2020.
On Google Books:
https://books.google.ca/books/about?id=jFQjEQAAQBAJ&redir_esc=y
On Google Play: https://play.google.com/store/books/details?id=jFQjEQAAQBAJ
The provided text introduces the Euclidean Algorithm, a method for finding the greatest common divisor (GCD) of two integers. The algorithm is presented both conceptually, as finding the smallest common unit of measurement, and procedurally, using a series of divisions and remainders. The text then explores the algorithm's application to line segments, highlighting the implicit assumption of a common unit of length. It concludes by acknowledging that the algorithm relies on the existence of a common unit (like the number 1 for integers) and may not be directly applicable to all pairs of line segments.
...more
8min
September 25, 2024 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 (http://www.ic.gc.ca/app/opic-cipo/cpyrghts/srch.do?lang=eng&page=1&searchCriteriaBean.textField1=1173734&searchCriteriaBean.column1=COP_REG_NUM&submitButton=Search&searchCriteriaBean.andOr1=and&searchCriteriaBean.textField2=&searchCriteriaBean.column2=TITLE&searchCriteriaBean.andOr2=and&searchCriteriaBean.textField3=&searchCriteriaBean.column3=TITLE&searchCriteriaBean.type=&searchCriteriaBean.dateStart=&searchCriteriaBean.dateEnd=&searchCriteriaBean.sortSpec=&searchCriteriaBean.maxDocCount=200&searchCriteriaBean.docsPerPage=10) , Ottawa, ISBN 9798685065292, 2020.
On Google Books:
https://books.google.ca/books/about?id=jFQjEQAAQBAJ&redir_esc=y
On Google Play: https://play.google.com/store/books/details?id=jFQjEQAAQBAJ
The text explores the historical development of methods used to estimate the distribution of prime numbers. It begins by highlighting the difficulties faced by mathematicians like Gauss in manually calculating prime numbers, especially for large sets. The text then delves into the idea of using logarithms to approximate the number of primes below a given number, a concept that Gauss himself explored. This leads into a discussion of the Prime Number Theorem, which provides a precise asymptotic formula for the distribution of prime numbers. Finally, the text touches upon the logarithmic integral as a refined approximation for the distribution of primes.
...more
8min
September 24, 2024 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 (http://www.ic.gc.ca/app/opic-cipo/cpyrghts/srch.do?lang=eng&page=1&searchCriteriaBean.textField1=1173734&searchCriteriaBean.column1=COP_REG_NUM&submitButton=Search&searchCriteriaBean.andOr1=and&searchCriteriaBean.textField2=&searchCriteriaBean.column2=TITLE&searchCriteriaBean.andOr2=and&searchCriteriaBean.textField3=&searchCriteriaBean.column3=TITLE&searchCriteriaBean.type=&searchCriteriaBean.dateStart=&searchCriteriaBean.dateEnd=&searchCriteriaBean.sortSpec=&searchCriteriaBean.maxDocCount=200&searchCriteriaBean.docsPerPage=10) , Ottawa, ISBN 9798685065292, 2020.
On Google Books:
https://books.google.ca/books/about?id=jFQjEQAAQBAJ&redir_esc=y
On Google Play: https://play.google.com/store/books/details?id=jFQjEQAAQBAJ
The text discusses Gauss's attempts to find a pattern in the distribution of prime numbers. The author examines Gauss's early experiments with counting primes and explores his eventual development of a formula to approximate the number of primes less than a given number. The text also highlights the limitations of this formula and the ongoing challenge of finding a precise mathematical expression for the distribution of primes. The author then discusses the Prime Number Theorem, which provides a more accurate approximation for the distribution of primes, and the logarithmic integral as an even better approximation. Finally, the text touches upon the implications of this problem for our understanding of mathematics and the potential need for new approaches to address it.
...more
9min
September 23, 2024 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 (http://www.ic.gc.ca/app/opic-cipo/cpyrghts/srch.do?lang=eng&page=1&searchCriteriaBean.textField1=1173734&searchCriteriaBean.column1=COP_REG_NUM&submitButton=Search&searchCriteriaBean.andOr1=and&searchCriteriaBean.textField2=&searchCriteriaBean.column2=TITLE&searchCriteriaBean.andOr2=and&searchCriteriaBean.textField3=&searchCriteriaBean.column3=TITLE&searchCriteriaBean.type=&searchCriteriaBean.dateStart=&searchCriteriaBean.dateEnd=&searchCriteriaBean.sortSpec=&searchCriteriaBean.maxDocCount=200&searchCriteriaBean.docsPerPage=10) , Ottawa, ISBN 9798685065292, 2020.
On Google Books:
https://books.google.ca/books/about?id=jFQjEQAAQBAJ&redir_esc=y
On Google Play: https://play.google.com/store/books/details?id=jFQjEQAAQBAJ
Summary
The text explores the concept of "mental experiments" in mathematics, arguing that mathematics, like the physical world, can be investigated through a process of experimentation and measurement. The author uses the problem of determining the distribution of prime numbers as an example, highlighting the need to define fundamental concepts like "multiplication" and "addition" before performing such mental experiments. The author concludes that these mental experiments can be performed with perfect accuracy, resulting in measurements that exactly match the "actual" mathematical reality.
...more
10min
September 22, 2024 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: https://play.google.com/store/books/details?id=jFQjEQAAQBAJ
The podcast explores the scientific method, focusing on its use in discovering and proving laws of nature. It emphasizes the importance of reproducible experiments, controlled environments, and accurate measurements. The author posits that scientists strive to identify underlying mathematical patterns within experimental data, even acknowledging the inevitable presence of errors. Ultimately, the goal is to communicate new discoveries through mathematical formulas and scientific publications.
...more
6min
September 22, 2024 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 framework that challenges traditional Euclidian geometry. The author, Nick Trif, proposes that points in space, typically viewed as dimensionless, should be considered as infinitesimal spheres. CPS Geometry posits that these spheres, arranged in a close-packing pattern, form the basis of space and can be used to understand various mathematical and scientific concepts. The text outlines the fundamental axioms of CPS Geometry, emphasizing its connection to number theory and arguing that it cannot be fully understood using the axiomatic approach of Euclidian geometry.
...more
9min

FAQs about The Geometry of Closed Packed Spheres:

How many episodes does The Geometry of Closed Packed Spheres have?

The podcast currently has 23 episodes available.