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A proof of the Kepler conjecture
 Math. Intelligencer
, 1994
"... This section describes the structure of the proof of ..."
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This section describes the structure of the proof of
Sphere Packings V
, 1997
"... Abstract. The Hales program to prove the Kepler conjecture on sphere packings consists of five steps, which if completed, will jointly comprise a proof of the conjecture. We carry out step five of the program, a proof that the local density of a certain combinatorial arrangement, the pentahedral pri ..."
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Abstract. The Hales program to prove the Kepler conjecture on sphere packings consists of five steps, which if completed, will jointly comprise a proof of the conjecture. We carry out step five of the program, a proof that the local density of a certain combinatorial arrangement, the pentahedral prism, is less than that of the facecentered cubic lattice packing. We prove various relations on the local density using computerbased interval arithmetic methods. Together, these relations imply the local density bound. 1.
Sphere Packings IV
 http://www.math.pitt.edu/ ∼ thales/ kepler98/sphere4.ps
, 1998
"... This paper is one of a series of papers devoted to the Kepler conjecture. This series began with [I], which proposed a line of research to prove the conjecture, and broke the conjecture into smaller conjectural steps which imply the Kepler conjecture. The steps were intended to be equal in difficult ..."
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This paper is one of a series of papers devoted to the Kepler conjecture. This series began with [I], which proposed a line of research to prove the conjecture, and broke the conjecture into smaller conjectural steps which imply the Kepler conjecture. The steps were intended to be equal in difficulty, although some have emerged as more difficult than others. This paper completes part of the fourth step. The main result is Theorem 4.4.
Sphere Packings III
 http://www.math.pitt.edu/ ∼ thales/ kepler98/sphere3.ps
, 1998
"... This paper is a continuation of the first two parts of this series ([I],[II]). It relies on the formulation of the Kepler conjecture in [F]. The terminology and notation of this paper are consistent with these earlier papers, and we refer to results from them by prefixing the relevant section number ..."
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This paper is a continuation of the first two parts of this series ([I],[II]). It relies on the formulation of the Kepler conjecture in [F]. The terminology and notation of this paper are consistent with these earlier papers, and we refer to results from them by prefixing the relevant section numbers with I, II, or F. Around each vertex is a modification of the Voronoi cell, called the V cell and a collection of quarters and quasiregular tetrahedra. These objects consititute the decomposition star at the vertex. A decomposition star may be decomposed into standard clusters. By definition, a standard cluster is the part of the given decomposition star that lies over a given standard region on the unit sphere.
The Life and Work of R. A. Rankin (19152001)
"... decades, one of the world’s foremost experts in modular forms, died on January 27, 2001 in Glasgow at the age of 85. He was one of the founding editors of The Ramanujan Journal. For this and the next issue of the The Ramanujan Journal, many wellknown mathematicians have prepared articles in Rankin’ ..."
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decades, one of the world’s foremost experts in modular forms, died on January 27, 2001 in Glasgow at the age of 85. He was one of the founding editors of The Ramanujan Journal. For this and the next issue of the The Ramanujan Journal, many wellknown mathematicians have prepared articles in Rankin’s memory. In this opening paper, we provide a short biography of Rankin and discuss some of his major contributions to mathematics. At the conclusion of this article, we provide a complete list of Rankin’s doctoral students and a complete bibliography of all of Rankin’s writings divided into