Results 1 to 10 of about 273 (99)
The Arrangement of the Osteons and Kepler’s Conjecture
Applied Sciences (Switzerland), 2023 The studies of bone tissue have mainly highlighted the morphometrical characteristics of the osteons, rather than their spatial distribution. This work aimed to verify if the topographical distribution of the osteons responds to geometrical order.
Marco Zedda
exaly +6 more sources
The symmetry of the Kepler problem, the inverse Ligon-Schaaf mapping and the Birkhoff conjecture. [PDF]
PLoS ONE, 2018 The Ligon-Schaaf regularization (LS mapping) was introduced in 1976 and has been used several times. However, we are not aware of any direct usage of the inverse mapping, perhaps since it appears at first sight to be quite complex, involves the use of a ...
Thomas Sumner Ligon
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A FORMAL PROOF OF THE KEPLER CONJECTURE [PDF]
Forum of Mathematics, Pi, 2017 This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project.
THOMAS HALES +21 more
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A Formulation of the Kepler Conjecture [PDF]
Discrete and Computational Geometry, 2006 23 pages.
Thomas C Hales, Hales Thomas C
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Historical Overview of the Kepler Conjecture [PDF]
Discrete and Computational Geometry, 2006 This paper is the first in a series of six papers devoted to the proof of the Kepler conjecture, which asserts that no packing of congruent balls in three dimensions has density greater than the face-centered cubic packing. After some preliminary comments about the face-centered cubic and hexagonal close packings, the history of the Kepler problem is ...
Thomas C Hales, Hales Thomas C
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A Revision of the Proof of the Kepler Conjecture [PDF]
Discrete and Computational Geometry, 2009 The Kepler conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space has density greater than that of the face-centered cubic packing. The original proof, announced in 1998 and published in 2006, is long and complex. The process of revision and review did not end with the publication of the proof.
Tobias Nipkow +2 more
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Bounds for Local Density of Sphere Packings and the Kepler Conjecture [PDF]
Discrete and Computational Geometry, 2002 27 pages, latex, 1 ...
Lagarias J C, J C Lagarias
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A proof of the Kepler conjecture [PDF]
Annals of Mathematics, 2005 Thomas C Hales
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Kepler’s Conjecture and the Dodecahedral Conjecture
Mitteilungen Der Deutschen Mathematiker-Vereinigung, 1996 Karoly Bezdek
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Prototyping "Systems that Explain Themselves" for Education [PDF]
Electronic Proceedings in Theoretical Computer Science, 2018 "Systems that Explain Themselves" appears a provocative wording, in particular in the context of mathematics education – it is as provocative as the idea of building educational software upon technology from computer theorem proving.
Alan Krempler, Walther Neuper
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