04. The Euclidian Algorithm

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The Geometry of Closed Packed Spheres

Nick Trif

23 episodes

2 days 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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04. The Euclidian Algorithm

The Geometry of Closed Packed Spheres

7 minutes 34 seconds

1 year ago

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.