16:30–17:20 Chuanming Zong The Sausage Conjecture 17:30 in memoriam Peter M. BETKE, P. 256 p. MathSciNet Google Scholar. re call that Betke and Henk [4] prove d L. M. Let Bd the unit ball in Ed with volume KJ. F. Fejes Toth made the sausage conjecture in´It is proved that for a densest packing of more than three d -balls, d geq 3 , where the density is measured by parametric density, the convex hull of their centers is either linear (a sausage) or at least three-dimensional. Further lattic in hige packingh dimensions 17s 1 C. Usually we permit boundary contact between the sets. A new continuation method for computing implicitly defined manifolds is presented, represented as a set of overlapping neighborhoods, and extended by an added neighborhood of a bounda. In -D for the arrangement of Hyperspheres whose Convex Hull has minimal Content is always a ``sausage'' (a set of Hyperspheres arranged with centers along a line), independent of the number of -spheres. Conjectures arise when one notices a pattern that holds true for many cases. Math. Technische Universität München. The. From the 42-dimensional space onwards, the sausage is always the closest arrangement, and the sausage disaster does not occur. Sierpinski pentatope video by Chris Edward Dupilka. 1) Move to the universe within; 2) Move to the universe next door. :. Skip to search form Skip to main content Skip to account menu. That’s quite a lot of four-dimensional apples. The Sausage Catastrophe of Mathematics If you want to avoid her, you have to flee into multidimensional spaces. Fejes Tóths Wurstvermutung in kleinen Dimensionen Download PDFMonatsh Math (2019) 188:611–620 Minimizing the mean projections of finite ρ-separable packings Károly Bezdek1,2. . Wills it is conjectured that, for alld5, linear arrangements of thek balls are best possible. It is not even about food at all. Introduction. Fejes Toth's Problem 189 12. ss Toth's sausage conjecture . 3], for any set of zones (not necessarily of the same width) covering the unit sphere. SLICES OF L. , Bk be k non-overlapping translates of the unid int d-bal euclideal Bn d-space Ed. • Bin packing: Locate a finite set of congruent balls in the smallest volume container of a specific kind. Fejes Tóth's sausage conjecture, says that for d ≧5 V ( S k + B d) ≦ V ( C k + B d In the paper partial results are given. . For the pizza lovers among us, I have less fortunate news. The conjecture was proposed by Fejes Tóth, and solved for dimensions >=42 by Betke et al. Introduction. The emphases are on the following five topics: the contact number problem (generalizing the problem of kissing numbers), lower bounds for Voronoi cells (studying. Gritzmann and J. Fejes Toth conjectured (cf. He conjectured that some individuals may be able to detect major calamities. Polyanskii was supported in part by ISF Grant No. Fejes Toth conjectured that in E d , d ≥ 5, the sausage arrangement is denser than any other packing of n unit balls. A finite lattice packing of a centrally symmetric convex body K in $$mathbb{R}$$ d is a family C+K for a finite subset C of a packing lattice Λ of K. Semantic Scholar extracted view of "Sausage-skin problems for finite coverings" by G. ) but of minimal size (volume) is looked The Sausage Conjecture (L. ss Toth's sausage conjecture . The Tóth Sausage Conjecture is a project in Universal Paperclips. [3]), the densest packing of n>2 unit balls in Ed, d^S, is the sausage arrangement; namely, the centers of the balls are collinear. 3 (Sausage Conjecture (L. The slider present during Stage 2 and Stage 3 controls the drones. A basic problem in the theory of finite packing is to determine, for a. , Bk be k non-overlapping translates of the unit d-ball Bd in. , Bk be k non-overlapping translates of the unid int d-bal euclideal Bn d-space Ed. L. Download to read the full article text Working on a manuscript? Avoid the common mistakes Author information. We also. For the pizza lovers among us, I have less fortunate news. Request PDF | On Nov 9, 2021, Jens-P. Tóth’s sausage conjecture is a partially solved major open problem [3]. ) but of minimal size (volume) is lookedThis gives considerable improvement to Fejes T6th's "sausage" conjecture in high dimensions. . . FEJES TOTH'S SAUSAGE CONJECTURE U. 3. F. The Sausage Catastrophe 214 Bibliography 219 Index . Acta Mathematica Hungarica - Über L. L. In this way we obtain a unified theory for finite and infinite. L. ss Toth's sausage conjecture . ) but of minimal size (volume) is lookedThe Sausage Conjecture (L. Fejes Tóth’s “sausage-conjecture” - Kleinschmidt, Peter, Pachner, U. Manuscripts should preferably contain the background of the problem and all references known to the author. Abstract. Max. When buying this will restart the game and give you a 10% boost to demand and a universe counter. a sausage arrangement in Ed and observed δ(Sd n) <δ(d) for all n, provided that the dimension dis at least 5. Wills. Creativity: The Tóth Sausage Conjecture and Donkey Space are near. 2), (2. We further show that the Dirichlet-Voronoi-cells are. math. 2. Contrary to what you might expect, this article is not actually about sausages. 10. 1007/BF01688487 Corpus ID: 123683426; Inequalities between the Kolmogorov and the Bernstein diameters in a Hilbert space @article{Pukhov1979InequalitiesBT, title={Inequalities between the Kolmogorov and the Bernstein diameters in a Hilbert space}, author={S. Dedicata 23 (1987) 59–66; MR 88h:52023. The meaning of TOGUE is lake trout. 99, 279-296 (1985) Mathemalik 9 by Springer-Verlag 1985 On Two Finite Covering Problems of Bambah, Rogers, Woods and ZassenhausHowever, as with the sausage catastrophe discussed in Section 1. This project costs negative 10,000 ops, which can normally only be obtained through Quantum Computing. Dekster 1 Acta Mathematica Hungarica volume 73 , pages 277–285 ( 1996 ) Cite this articleSausage conjecture The name sausage comes from the mathematician László Fejes Tóth, who established the sausage conjecture in 1975. . . Fejes Tóth [9] states that indimensions d 5, the optimal finite packingisreachedbyasausage. Let Bd the unit ball in Ed with volume KJ. The sausage conjecture has also been verified with respect to certain restriction on the packings sets, e. IfQ has minimali-dimensional projection, 1≤i<d then we prove thatQ is approximately a sphere. ss Toth's sausage conjecture . and the Sausage Conjectureof L. Fejes Tóth) states that in dimensions d ≥ 5, the densest packing of any finite number of spheres in R^d occurs if and only if the spheres are all packed in a line, i. This has been. (1994) and Betke and Henk (1998). We show that for any acute ϕ, there exists a covering of S d by spherical balls of radius ϕ such that no point is covered more than 400d ln d times. That is, the sausage catastrophe no longer occurs once we go above 4 dimensions. Period. The Universe Within is a project in Universal Paperclips. s Toth's sausage conjecture . Wills (2. The total width of any set of zones covering the sphereAn upper bound for the “sausage catastrophe” of dense sphere packings in 4-space is given. Here we optimize the methods developed in [BHW94], [BHW95] for the special A conjecture is a statement that mathematicians think could be true, but which no one has yet proved or disproved. TzafririWe show that the sausage conjecture of László Fejes Tóth on finite sphere packings is true in dimension 42 and above. Click on the article title to read more. Packings and coverings have been considered in various spaces and on. Monatsh Math (2019) 188:611–620 Minimizing the mean projections of finite ρ-separable packings Károly Bezdek1,2. The optimal arrangement of spheres can be investigated in any dimension. 4, Conjecture 5] and the arXiv version of [AK12, Conjecture 8. up the idea of Zong’s proof in [11] and show that the “spherical conjecture” is also valid in Minkowski Geometry. and the Sausage Conjectureof L. ( 1994 ) which was later improved to d ≥. Z. The first two of these are related to the Gauss–Bonnet and Steiner parallel formulae for spherical polytopes, while the third is completely new. 1007/BF01688487 Corpus ID: 123683426; Inequalities between the Kolmogorov and the Bernstein diameters in a Hilbert space @article{Pukhov1979InequalitiesBT, title={Inequalities between the Kolmogorov and the Bernstein diameters in a Hilbert space}, author={S. Let Bd the unit ball in Ed with volume KJ. LAIN E and B NICOLAENKO. M. AbstractIn 1975, L. Sci. 14 articles in this issue. Introduction. CON WAY and N. Fejes T oth [25] claims that for any number of balls, a sausage con guration is always best possible, provided d 5. In this paper we give a short survey on e cient algorithms for Steiner trees and paths packing problems in planar graphs We particularly concentrate on recent results The rst result is. CONWAYandN. up the idea of Zong’s proof in [11] and show that the “spherical conjecture” is also valid in Minkowski Geometry. The conjecture states that in n dimensions for n≥5 the arrangement of n-hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a line), independent of the number of n-spheres. If you choose the universe within, you restart the game on "Universe 1, Sim 2", with all functions appearing the same. Swarm Gifts is a general resource that can be spent on increasing processors and memory, and will eventually become your main source of both. Fejes Tóth's sausage conjecture - Volume 29 Issue 2. The r-ball body generated by a given set in E d is the intersection of balls of radius r centered at the points of the given set. WILLS. In 1975, L. . 2 Pizza packing. There was not eve an reasonable conjecture. In higher dimensions, L. BRAUNER, C. Acceptance of the Drifters' proposal leads to two choices. In the two dimensional space, the container is usually a circle [8], an equilateral triangle [14] or a square [15]. He conjectured in 1943 that the. In 1975, L. Search. The sausage conjecture holds for convex hulls of moderately bent sausages B. Introduction. Sign In. Partial results about this conjecture are contained inPacking problems have been investigated in mathematics since centuries. §1. If the number of equal spherical balls. Kuperburg, On packing the plane with congruent copies of a convex body, in [BF], 317–329; MR 88j:52038. Fejes Tóth's sausage…. For n∈ N and d≥ 5, δ(d,n) = δ(Sd n). Đăng nhập . The $r$-ball body generated by a given set in ${mathbb E}^d$ is the intersection of balls of radius. ) + p K ) > V(conv(Sn) + p K ) , where C n is a packing set with respect to K and S. Trust is the main upgrade measure of Stage 1. L. In 1975, L. The cardinality of S is not known beforehand which makes the problem very difficult, and the focus of this chapter is on a better. Click on the title to browse this issueThe sausage conjecture holds for convex hulls of moderately bent sausages @article{Dekster1996TheSC, title={The sausage conjecture holds for convex hulls of moderately bent sausages}, author={Boris V. BeitrAlgebraGeom as possible”: The first one leads to so called bin packings where a container (bin) of a prescribed shape (ball, simplex, cube, etc. The Sausage Catastrophe (J. Fejes Toth conjectured that in Ed, d ≥ 5, the sausage arrangement is denser than any other packing of n unit balls. AMS 27 (1992). 4. HenkIntroduction. In this paper, we settle the case when the inner m-radius of Cn is at least. Fejes T´ oth’s sausage conjectur e for d ≥ 42 acc ording to which the smallest volume of the convex hull of n non-overlapping unit balls in E d is. Projects are available for each of the game's three stages, after producing 2000 paperclips. Mh. 19. GustedtOn the Sausage Catastrophe in 4 Dimensions Ji Hoon Chun∗ Abstract The Sausage Catastrophe of J. Consider an arrangement of $n$ congruent zones on the $d$-dimensional unit sphere $S^{d-1}$, where a zone is the intersection of an origin symmetric Euclidean plank. space and formulated the following conjecture: for n ~ 5 the volume of the convex hull of k non-overlapping unit balls attains its minimum if the centres of the balls are equally spaced on a line with distance 2, so that the convex hull of the balls becomes a "sausage". AbstractIn 1975, L. Kuperburg, An inequality linking packing and covering densities of plane convex bodies, Geom. Trust is the main upgrade measure of Stage 1. Fejes Tóth also formulated the generalized conjecture, which has been reiterated in [BMP05, Chapter 3. Laszlo Fejes Toth 198 13. text; Similar works. B d denotes the d-dimensional unit ball with boundary S d−1 and. HADWIGER and J. The Tóth Sausage Conjecture is a project in Universal Paperclips. Fejes Toth conjectured that in E d , d ≥ 5, the sausage arrangement is denser than any other packing of n unit balls. This has been known if the convex hull C n of the centers has. LAIN E and B NICOLAENKO. L. For finite coverings in euclidean d -space E d we introduce a parametric density function. Your first playthrough was World 1, Sim. This is also true for restrictions to lattice packings. The main object of this note is to prove that in three-space the sausage arrangement is the densest packing of four unit balls. Rejection of the Drifters' proposal leads to their elimination. , the problem of finding k vertex-disjoint. The Spherical Conjecture The Sausage Conjecture The Sausage Catastrophe Sign up or login using form at top of the. A SLOANE. Close this message to accept cookies or find out how to manage your cookie settings. 1162/15, 936/16. 2. Donkey Space is a project in Universal Paperclips. 5 The CriticalRadius for Packings and Coverings 300 10. In this. txt) or view presentation slides online. To put this in more concrete terms, let Ed denote the Euclidean d. Pachner J. Fejes Toth conjectured that in Ed, d ≥ 5, the sausage arrangement is denser than any other packing of n unit. Based on the fact that the mean width is. When is it possible to pack the sets X 1, X 2,… into a given “container” X? This is the typical form of a packing problem; we seek conditions on the sets such that disjoint congruent copies (or perhaps translates) of the X. 4 Asymptotic Density for Packings and Coverings 296 10. In particular they characterize the equality cases of the corresponding linear refinements of both the isoperimetric inequality and Urysohn’s inequality. Let be k non-overlapping translates of the unit d -ball B d in euclidean d -space E d . Pukhov}, journal={Mathematical notes of the Academy of Sciences of the. Show abstract. • Bin packing: Locate a finite set of congruent balls in the smallest volume container of a specific kind. 453 (1994) 165-191 and the MathWorld Sausage Conjecture Page). . Fejes Tóth and J. We show that the sausage conjecture of László Fejes Tóth on finite sphere packings is true in dimension 42 and above. [4] E. In the paper several partial results are given to support both sausage conjectures and some relations between finite and infinite (space) packing and covering are investigated. • Bin packing: Locate a finite set of congruent spheres in the smallest volume container of a specific kind. GRITZMAN AN JD. Further, we prove that, for every convex bodyK and ρ<1/32d−2,V(conv(Cn)+ρK)≥V(conv(Sn)+ρK), whereCn is a packing set with respect toK andSn is a minimal “sausage” arrangement ofK, holds. Further o solutionf the Falkner-Ska. Wills. , B d [p N, λ 2] are pairwise non-overlapping in E d then (19) V d conv ⋃ i = 1 N B d p i, λ 2 ≥ (N − 1) λ λ 2 d − 1 κ d − 1 + λ 2 d. . IfQ has minimali-dimensional projection, 1≤i<d then we prove thatQ is approximately a sphere. Community content is available under CC BY-NC-SA unless otherwise noted. KLEINSCHMIDT, U. This fact is called Thue’s Theorem but had been shown for lattices already by Lagrange in 1773 and a complete proof is due to Fejes Tóth. [9]) that the densest pack ing of n > 2 unit balls in Ed, d > 5, is the sausage arrangement; namely the centers are collinear. BAKER. Mathematika, 29 (1982), 194. It is not even about food at all. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with. 1This gives considerable improvement to Fejes Tóth's “sausage” conjecture in high dimensions. On L. Contrary to what you might expect, this article is not actually about sausages. Limit yourself to 6 processors, and sink everything extra on memory. However, instead of occurring at n = 56, the transition from sausages to clusters is conjectured to happen only at around 377,000 spheres. View details (2 authors) Discrete and Computational Geometry. Fejes Toth by showing that the minimum gap size of a packing of unit balls in IR3 is 5/3 1 = 0. A zone of width ω on the unit sphere is the set of points within spherical distance ω/2 of a given great circle. V. 1007/BF01955730 Corpus ID: 119825877; On the density of finite packings @article{Wills1985OnTD, title={On the density of finite packings}, author={J{"o}rg M. This has been known if the convex hull C n of the centers has. • Bin packing: Locate a finite set of congruent balls in the smallest volume container of a specific kind. Projects in the ending sequence are unlocked in order, additionally they all have no cost. A SLOANE. 5) (Betke, Gritzmann and Wills 1982) dim Q ^ 9 and (Betke and Gritzmann 1984) Q is a lattice zonotope (Betke and Gritzmann 1986) Q is a regular simplex (G. SLOANE. In n-dimensional Euclidean space with n > 5 the volume of the convex hull of m non-overlapping unit balls is at least 2(m - 1)con_ 1 + co, where co i indicates the volume of the i-dimensional unit ball. F ejes Tóth, 1975)) . W. H. Ulrich Betke | Discrete and Computational Geometry | We show that the sausage conjecture of Laszlo Fejes Toth on finite sphere packings is true in dimens. Wills (1983) is the observation that in d = 3 and d = 4, the densest packing of nSemantic Scholar extracted view of "Note on Shortest and Nearest Lattice Vectors" by M. The Tóth Sausage Conjecture is a project in Universal Paperclips. 2 Planar Packings for Reasonably Large 78 ixBeitrAlgebraGeom as possible”: The first one leads to so called bin packings where a container (bin) of a prescribed shape (ball, simplex, cube, etc. Extremal Properties AbstractIn 1975, L. Furthermore, led denott V e the d-volume. The first is K. An upper bound for the “sausage catastrophe” of dense sphere packings in 4-space is given. Message from the Emperor of Drift is unlocked when you explore the entire universe and use all the matter to make paperclips. On a metrical theorem of Weyl 22 29. A SLOANE. Let C k denote the convex hull of their centres ank bde le a segment S t of length 2(/c— 1). On a metrical theorem of Weyl 22 29. 409/16, and by the Russian Foundation for Basic Research through Grant Nos. It is not even about food at all. BOS. N M. F. However, just because a pattern holds true for many cases does not mean that the pattern will hold. The first chip costs an additional 10,000. Quantum Computing is a project in Universal Paperclips. Betke, Henk, and Wills [7] proved for sufficiently high dimensions Fejes Toth's sausage conjecture. Fejes Toth made the sausage conjecture in´Abstract Let E d denote the d-dimensional Euclidean space. In 1975, L. ON L. Consider the convex hullQ ofn non-overlapping translates of a convex bodyC inEd,n be large. com Dictionary, Merriam-Webster, 17 Nov. Simplex/hyperplane intersection. Projects are a primary category of functions in Universal Paperclips. Consider the convex hullQ ofn non-overlapping translates of a convex bodyC inEd,n be large. DOI: 10. LAIN E and B NICOLAENKO. Kleinschmidt U. Constructs a tiling of ten-dimensional space by unit hypercubes no two of which meet face-to-face, contradicting a conjecture of Keller that any tiling included two face-to-face cubes. Further lattic in hige packingh dimensions 17s 1 C M. In the two dimensional space, the container is usually a circle [8], an equilateral triangle [14] or a square [15]. Projects are available for each of the game's three stages, after producing 2000 paperclips. Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Instead, the sausage catastrophe is a mathematical phenomenon that occurs when studying the theory of finite sphere packing. In this paper we present a linear-time algorithm for the vertex-disjoint Two-Face Paths Problem in planar graphs, i. SLICES OF L. a sausage arrangement in Ed and observed δ(Sd n) <δ(d) for all n, provided that the dimension dis at least 5. Tóth’s sausage conjecture is a partially solved major open problem [3]. For ϱ>0 the density δ (C;K,ϱ) is defined by δ(C;K,ϱ) = card C·V(K)/V(conv C+ϱK). . Let d 5 and n2N, then Sd n = (d;n), and the maximum density (d;n) is only obtained with a sausage arrangement. All Activity; Home ; Philosophy ; General Philosophy ; Are there Universal Laws? Can you break them?Diagrams mapping the flow of the game Universal Paperclips - paperclips-diagrams/paperclips-diagram-stage2. . 4 Relationships between types of packing. 266 BeitrAlgebraGeom(2021)62:265–280 as possible”: The first one leads to so called bin packings where a container (bin) of a prescribed shape (ball, simplex, cube, etc. Dive in!When you conjecture, you form an opinion or reach a conclusion on the basis of information that is not certain or complete. Throughout this paper E denotes the d-dimensional Euclidean space and the set of all centrally Symmetrie convex bodies K a E compact convex sets with K = — Kwith non-empty interior (int (K) φ 0) is denoted by J^0. Keller's cube-tiling conjecture is false in high dimensions, J. M. Finite Sphere Packings 199 13. 4 Sausage catastrophe. BETKE, P. (+1 Trust) Coherent Extrapolated Volition: 500 creat 20,000 ops 3,000 yomi 1 yomi +1 Trust (todo) Male Pattern Baldness: 20,000 ops Coherent. N M. SLICES OF L. 1007/pl00009341. Lagarias and P. Betke et al. 2. Throughout this paper E denotes the d-dimensional Euclidean space and the set of all centrally Symmetrie convex bodies K a E compact convex sets with K = — Kwith non-empty interior (int (K) φ 0) is denoted by J^0. The conjecture was proposed by László Fejes Tóth, and solved for dimensions n. This has been known if the convex hull Cn of the centers has low dimension. [3]), the densest packing of n>2 unit balls in Ed, d^S, is the sausage arrangement; namely, the centers of the balls are collinear. Math. N M. Letk non-overlapping translates of the unitd-ballBd⊂Ed be given, letCk be the convex hull of their centers, letSk be a segment of length 2(k−1) and letV denote the volume. N M. M. (+1 Trust) Coherent Extrapolated Volition 500 creat 20,000 ops 3,000 yomi 1 yomi +1 Trust (todo) Male Pattern Baldness 20,000 ops Coherent Extrapolated Volition A. ppt), PDF File (. The Hadwiger problem In d-dimensions, define L(d) to be the largest integer n for. In 1975, L. In n dimensions for n>=5 the arrangement of hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a line), independent of the number of n-spheres. DOI: 10. A packing of translates of a convex body in the d-dimensional Euclidean space $${{mathrm{mathbb {E}}}}^d$$Ed is said to be totally separable if any two packing. Conjecture 1. e. The sausage conjecture holds for all dimensions d≥ 42. 1. For a given convex body K in ℝd, let Dn be the compact convex set of maximal mean width whose 1-skeleton can be covered by n congruent copies of K. 1984. In the two-dimensional space, the container is usually a circle [9], an equilateral triangle [15] or a. §1. 8 Ball Packings 309 A first step in verifying the sausage conjecture was done in [B HW94]: The sausage conjecture holds for all d ≥ 13 , 387. Monatshdte tttr Mh. 2. Nhớ mật khẩu. Radii and the Sausage Conjecture - Volume 38 Issue 2 Online purchasing will be unavailable on Sunday 24th July between 8:00 and 13:30 BST due to essential maintenance work. Thus L. In 1998 they proved that from a dimension of 42 on the sausage conjecture actually applies. Last time updated on 10/22/2014. . A basic problem of finite packing and covering is to determine, for a given number ofk unit balls in Euclideand-spaceEd, (1) the minimal volume of all convex bodies into which thek balls. There exist «o^4 and «t suchVolume 47, issue 2-3, December 1984. See moreThe conjecture was proposed by Fejes Tóth, and solved for dimensions >=42 by Betke et al. BAKER. Slice of L Feje. László Fejes Tóth, a 20th-century Hungarian geometer, considered the Voronoi decomposition of any given packing of unit spheres. A SLOANE. An upper bound for the “sausage catastrophe” of dense sphere packings in 4-space is given. 1016/0012-365X(86)90188-3 Corpus ID: 44874167; An application of valuation theory to two problems in discrete geometry @article{Betke1986AnAO, title={An application of valuation theory to two problems in discrete geometry}, author={Ulrich Betke and Peter Gritzmann}, journal={Discret. Message from the Emperor of Drift is unlocked when you explore the entire universe and use all the matter. The length of the manuscripts should not exceed two double-spaced type-written. Sausage Conjecture 200 creat 200 creat Tubes within tubes within tubes. Department of Mathematics. Abstract. Fejes Toth conjectured (cf. Wills, SiegenThis article sketches the proofs of two theorems about sphere packings in Euclidean 3-space. J. Fejes Tóth [9] states that indimensions d 5, the optimal finite packingisreachedbyasausage. The slider present during Stage 2 and Stage 3 controls the drones. M. Fejes Tóth for the dimensions between 5 and 41. lated in 1975 his famous sausage conjecture, claiming that for dimensions ≥ 5 and any(!) number of unit balls, a linear arrangement of the balls, i. We call the packing $$mathcal P$$ P of translates of. New York: Springer, 1999. Our main tool is a generalization of a result of Davenport that bounds the number of lattice points in terms of volumes of suitable projections. Math. Feodor-Lynen Forschungsstipendium der Alexander von Humboldt-Stiftung. Đăng nhập bằng google.