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Least Action Principle of Crystal Formation of Dense Packing Type & the Proof of Kepler's Conjecture

Least Action Principle of Crystal Formation of Dense Packing Type & the Proof of Kepler's Conjecture

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Least Action Principle of Crystal Formation of Dense Packing Type & the Proof of Kepler's Conjecture

Least Action Principle of Crystal Formation of Dense Packing Type & the Proof of Kepler's Conjecture

4.85 29,693 ratings · 6,462 reviews
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Overview: The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal "known density" of B/√18. In 1611, Johannes Kepler had already "conjectured" that B/√18 should be the optimal "density" of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that B/√18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry.

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Book details & editions

ISBN
1587377
Publication date
March 15, 2002
Pages
N/A pages
Reading Options
PDF · EPUB · Mobi
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Wu Yi Hsiang
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Wu Yi Hsiang is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Wu Yi Hsiang can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Dorothy Thomas
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Betty Nelson
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes.
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I find myself somewhat conflicted. Certain acts were fascinating, while others felt like a slight endeavor to complete. A fair 3 stars.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Richard Roberts
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
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It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
Elizabeth Thomas
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
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Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Jessica Martin
Jessica Martin December 12, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Stephanie Sanchez
Stephanie Sanchez February 27, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Dorothy Torres
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Edward Lee
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
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