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List Of Shapes With Known Packing Constant
The packing constant of a geometric body is the largest average density achieved by packing arrangements of Congruence (geometry), congruent copies of the body. For most bodies the value of the packing constant is unknown. The following is a list of bodies in Euclidean spaces whose packing constant is known. László Fejes Tóth, Fejes Tóth proved that in the plane, a point reflection, point symmetric body has a packing constant that is equal to its translation (geometry), translative packing constant and its Bravais lattice, lattice packing constant. Therefore, any such body for which the lattice packing constant was previously known, such as any ellipse, consequently has a known packing constant. In addition to these bodies, the packing constants of n-sphere, hyperspheres in 8 and 24 dimensions are almost exactly known. References {{DEFAULTSORT:Shapes with known packing constant Packing problems Discrete geometry Mathematics-related lists ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Packing Constant
A packing density or packing fraction of a packing in some space is the fraction (mathematics), fraction of the space filled by the figures making up the packing. In simplest terms, this is the ratio of the volume of bodies in a space to the volume of the space itself. In packing problems, the objective is usually to obtain a packing of the greatest possible density. In compact spaces If are measurable subsets of a Compact space, compact measure space and their interiors pairwise do not intersect, then the collection is a packing in and its packing density is :\eta = \frac. In Euclidean space If the space being packed is infinite in measure, such as Euclidean space, it is customary to define the density as the limit of densities exhibited in balls of larger and larger radii. If is the ball of radius centered at the origin, then the density of a packing is :\eta = \lim_\frac. Since this limit does not always exist, it is also useful to define the upper and lower dens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Callister Hales
Thomas Callister Hales (born June 4, 1958) is an American mathematician working in the areas of representation theory, discrete geometry, and formal verification. In representation theory he is known for his work on the Langlands program and the proof of the fundamental lemma over the group Sp(4) (many of his ideas were incorporated into the final proof of the fundamental lemma, due to Ngô Bảo Châu). In discrete geometry, he settled the Kepler conjecture on the density of sphere packings and the honeycomb conjecture. In 2014, he announced the completion of the Flyspeck Project, which formally verified the correctness of his proof of the Kepler conjecture. Biography He received his Ph.D. from Princeton University in 1986, his dissertation was titled ''The Subregular Germ of Orbital Integrals''. Hales taught at Harvard University and the University of Chicago, and from 1993 and 2002 he worked at the University of Michigan. In 1998, Hales submitted his paper on the computer-ai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete & Computational Geometry
'' Discrete & Computational Geometry'' is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational geometry. Abstracting and indexing The journal is indexed in: * ''Mathematical Reviews'' * ''Zentralblatt MATH'' * ''Science Citation Index The Science Citation Index Expanded – previously entitled Science Citation Index – is a citation index originally produced by the Institute for Scientific Information (ISI) and created by Eugene Garfield. It was officially launched in 1964 ...'' * '' Current Contents''/Engineering, Computing and Technology Notable articles The articles by Gil Kalai with a proof of a subexponential upper bound on the diameter of a polyhedron and by Samuel Ferguson on the Kepler conjecture, both published in Discrete & Computational geometry, earned their author the Fulkerson Prize. References Externa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematika
''Mathematika'' is a peer-reviewed mathematics journal that publishes both pure and applied mathematical articles. The journal was founded by Harold Davenport in the 1950s. The journal is published by the London Mathematical Society, on behalf of the journal's owner University College London. Indexing and abstracting According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 0.844. The journal in indexing in the following bibliographic databases: * MathSciNet * Science Citation Index Expanded * Web of Science * Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastruct ... References {{reflist London Mathematical Society Mathematics education in the United Kingdom Mathematics journals Publications established in 1954 Quarterly journals Wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Włodzimierz Kuperberg
Włodzimierz Kuperberg (born January 19, 1941) is a professor of mathematics at Auburn University, with research interests in geometry and topology. Biography Although Kuperberg is Polish-American, he was born in what is now Belarus, where his parents and older siblings had traveled east to escape World War II. In 1946, the family returned to Poland, resettling in Szczecin, where Kuperberg grew up. He began his studies at the University of Warsaw in 1959, and received his Ph.D. from the same institution in 1969, under the supervision of Karol Borsuk. During his time at Warsaw, he published three high school textbooks in Polish. Kuperberg left Poland due to the anti-semitic aspects of the 1967-1968 Polish political crisis, and worked at Stockholm University until 1972, when he assumed a visiting position at the University of Houston. In 1974, Kuperberg took a position at Auburn where he remains. Kuperberg married mathematician Krystyna Kuperberg in 1964, and their son Greg Kuperbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
András Bezdek
András () is a Hungarian masculine given name, the Hungarian form of ''Andrew''. Notable people with the name include: * András Ádám-Stolpa (born 1921), Hungarian tennis player * András Adorján (born 1950), Hungarian writer * András Ágoston (21st century), Hungarian Serbian politician * András Arató (born 1945), also known as Hide the Pain Harold, internet meme, stock photo model, and electrical engineer * András Balczó (born 1938), Hungarian modern pentathlete * András Baronyi (1892-1944), Hungarian swimmer * András Báthory (1562 or 1563–1599), Prince of Transylvania * András Beck (1911-1985), Hungarian sculptor * András Benkei (born 1923), Hungarian politician * András Béres (1924-1993), Hungarian footballer * András Bethlen (1847–1898), Hungarian politician * András Bodnár (born 1942), Hungarian water polo player * András Botos (born 1952), Hungarian boxer * András Csáki (born 1981), Hungarian musician * András Debreceni (born 1989), Hungarian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Red Cylinder
Red is the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength of approximately 625–740 nanometres. It is a primary color in the RGB color model and a secondary color (made from magenta and yellow) in the CMYK color model, and is the complementary color of cyan. Reds range from the brilliant yellow-tinged scarlet and vermillion to bluish-red crimson, and vary in shade from the pale red pink to the dark red burgundy. Red pigment made from ochre was one of the first colors used in prehistoric art. The Ancient Egyptians and Mayans colored their faces red in ceremonies; Roman generals had their bodies colored red to celebrate victories. It was also an important color in China, where it was used to color early pottery and later the gates and walls of palaces. In the Renaissance, the brilliant red costumes for the nobility and wealthy were dyed with kermes and cochineal. The 19th century brought the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kepler Conjecture
The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements. The density of these arrangements is around 74.05%. In 1998, Thomas Hales, following an approach suggested by , announced that he had a proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving the checking of many individual cases using complex computer calculations. Referees said that they were "99% certain" of the correctness of Hales' proof, and the Kepler conjecture was accepted as a theorem. In 2014, the Flyspeck project team, headed by Hales, announced the completion of a formal proof of the Kepler conjecture using a combination of the Isabelle and HOL Light proof assis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FCC Closed Packing Tetrahedron (20)
The Federal Communications Commission (FCC) is an independent agency of the United States federal government that regulates communications by radio, television, wire, satellite, and cable across the United States. The FCC maintains jurisdiction over the areas of broadband access, fair competition, radio frequency use, media responsibility, public safety, and homeland security. The FCC was formed by the Communications Act of 1934 to replace the radio regulation functions of the Federal Radio Commission. The FCC took over wire communication regulation from the Interstate Commerce Commission. The FCC's mandated jurisdiction covers the 50 states, the District of Columbia, and the territories of the United States. The FCC also provides varied degrees of cooperation, oversight, and leadership for similar communications bodies in other countries of North America. The FCC is funded entirely by regulatory fees. It has an estimated fiscal-2022 budget of US $388 million. It has 1,482 fede ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruth Silverman
Ruth Silverman (born 1936 or 1937, died April 25, 2011) was an American mathematician and computer scientist known for her research in computational geometry. She was one of the original founders of the Association for Women in Mathematics in 1971. Education and career Silverman completed a Ph.D. in 1970 at the University of Washington. She was a faculty member at the New Jersey Institute of Technology, an associate professor at Southern Connecticut State College, a computer science instructor at the University of the District of Columbia, and a researcher in the Center for Automation Research at the University of Maryland, College Park. Contributions Silverman's dissertation, ''Decomposition of plane convex sets'', concerned the characterization of compact convex sets in the Euclidean plane that cannot be formed as Minkowski sums of simpler sets. She became known for her research in computational geometry and particular for highly cited publications on k-means clusterin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Mount
David Mount is a professor at the University of Maryland, College Park department of computer science whose research is in computational geometry. Biography Mount received a B.S. in Computer Science at Purdue University in 1977 and received his Ph.D. in Computer Science at Purdue University in 1983 under the advisement of Christoph Hoffmann. He began teaching at the University of Maryland in 1984 and is Professor in the department of Computer Science there. As a teacher, he has won the University of Maryland, College of Computer Mathematical and Physical Sciences Dean's Award for Excellence in Teaching in 2005 and 1997 as well as other teaching awards including the Hong Kong Science and Technology, School of Engineering Award for Teaching Excellence Appreciation in 2001. Research Mounts's main area of research is computational geometry, which is the branch of algorithms devoted to solving problems of a geometric nature. This field includes problems from classic geometry, l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Decagon
In geometry, a decagon (from the Greek δέκα ''déka'' and γωνία ''gonía,'' "ten angles") is a ten-sided polygon or 10-gon.. The total sum of the interior angles of a simple decagon is 1440°. A self-intersecting ''regular decagon'' is known as a decagram. Regular decagon A ''regular decagon'' has all sides of equal length and each internal angle will always be equal to 144°. Its Schläfli symbol is and can also be constructed as a truncated pentagon, t, a quasiregular decagon alternating two types of edges. Side length The picture shows a regular decagon with side length a and radius R of the circumscribed circle. * The triangle E_E_1M has to equally long legs with length R and a base with length a * The circle around E_1 with radius a intersects ]M\,E_ in a point P (not designated in the picture). * Now the triangle \; is a isosceles triangle">/math> in a point P (not designated in the picture). * Now the triangle \; is a isosceles triangle with verte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
