03. Gauss Estimation An Epistemological Problem

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The Geometry of Closed Packed Spheres

Nick Trif

23 episodes

1 day ago

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 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.

Mathematics

Science

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Mathematics

Science

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03. Gauss Estimation An Epistemological Problem

The Geometry of Closed Packed Spheres

7 minutes 55 seconds

1 year ago

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.