Forsidebilde av showet The Geometry of Closed Packed Spheres

The Geometry of Closed Packed Spheres

Podkast av Nick Trif

engelsk

Teknologi og vitenskap

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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.

Alle episoder

23 Episoder

episode 17. Lines Patterns in Space cover

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 investigates patterns formed by lines emanating from a central point, analyzing these patterns based on the surrounding layers of points, which are arranged in cuboctahedron structures. The text also considers how these patterns arise from the arrangement of rhombic dodecahedrons, which fill space in CPS Geometry. The text concludes by highlighting the potential for further exploration of these line patterns and their connection to complex analysis concepts such as Möbius transformations.

17. okt. 2024 - 8 min
episode 16. The Fibonacci Sequence cover

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, approximately 1.618, that appears in various natural and mathematical phenomena. The source shows that the ratio of consecutive terms in the Fibonacci sequence approaches the Golden Ratio as the sequence progresses. It then explores the relationship between the Golden Ratio and the Close Packing of Spheres (CPS) geometry, which is a system for studying the arrangement of spheres in three-dimensional space. The source argues that the CPS geometry provides a geometric interpretation of the Golden Ratio and the Fibonacci sequence, demonstrating that the relationship between these concepts is not just a mathematical curiosity but has a basis in the natural world.

16. okt. 2024 - 8 min
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