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Tammes Problem
In geometry, the Tammes problem is a problem in circle packing, packing a given number of points on the surface of a sphere such that the minimum distance between points is maximized. It is named after the Dutch botanist Pieter Merkus Lambertus Tammes (the nephew of pioneering botanist Jantina Tammes) who posed the problem in his 1930 doctoral dissertation on the distribution of pores on pollen grains. It can be viewed as a particular special case of the Thomson problem#Generalizations, generalized Thomson problem of minimizing the total Coulomb force of electrons in a spherical arrangement. Thus far, solutions have been proven only for small numbers of circles: 3 through 14, and 24. There are conjectured solutions for many other cases, including those in higher dimensions. See also * Spherical code * Kissing number problem * Cylinder sphere packing, Cylinder sphere packings References Bibliography ; Journal articles * * * * * ; Books * * External links * . P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tammes Cropped
Jantina "Tine" Tammes (; 23 June 1871 – 20 September 1947) was a Dutch botanist and geneticist and the first professor of genetics in the Netherlands. Early life and education Tammes was born on 23 June 1871 in Groningen in the Netherlands. She was the daughter of cocoa manufacturer Beerend Tammes and Swaantje Pot. She had a sister and four brothers, and was the aunt of the international lawyer Arnold Tammes and the botanist Pieter Merkus Lambertus Tammes, after the Tammes problem in mathematics is named. After graduating from the high school for girls in Groningen and taking private lessons in mathematics, physics and chemistry, she enrolled at the University of Groningen in 1890 as one of just eleven female students. She was allowed to attend lectures but not to take any examinations, although she was awarded a teaching diploma. Research career In 1897 Tammes was appointed as an assistant to Jan Willem Moll, professor of botany at the University of Groningen. Through his m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cylinder Sphere Packing
Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder of specified diameter and length. For cylinders with diameters on the same order of magnitude as the spheres, such packings result in what are called columnar structures. These problems are studied extensively in the context of biology, nanoscience, materials science, and so forth due to the analogous assembly of small particles (like cells and atoms) into cylindrical crystalline structures. The book "Columnar Structures of Spheres: Fundamentals and Applications" serves as a notable contributions to this field of study. Authored by Winkelmann and Chan, the book reviews theoretical foundations and practical applications of densely packed spheres within cylindrical confinements. Appearance in science Columnar structures appear in various research fields on a broad range of length scales from metres down to the nanoscale. On the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Geometry
300px, A sphere with a spherical triangle on it. Spherical geometry or spherics () is the geometry of the two-dimensional surface of a sphere or the -dimensional surface of higher dimensional spheres. Long studied for its practical applications to astronomy, navigation, and geodesy, spherical geometry and the metrical tools of spherical trigonometry are in many respects analogous to Euclidean plane geometry and trigonometry, but also have some important differences. The sphere can be studied either ''extrinsically'' as a surface embedded in 3-dimensional Euclidean space (part of the study of solid geometry), or ''intrinsically'' using methods that only involve the surface itself without reference to any surrounding space. Principles In plane (Euclidean) geometry, the basic concepts are points and (straight) lines. In spherical geometry, the basic concepts are points and great circles. However, two great circles on a plane intersect in two antipodal points, unlike coplan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Packing
In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap. The associated ''packing density'', , of an arrangement is the proportion of the surface covered by the circles. Generalisations can be made to higher dimensions – this is called ''sphere packing'', which usually deals only with identical spheres. The branch of mathematics generally known as "circle packing" is concerned with the geometry and combinatorics of packings of arbitrarily-sized circles: these give rise to discrete analogs of conformal mapping, Riemann surfaces and the like. Densest packing In the two-dimensional Euclidean plane, Joseph Louis Lagrange proved in 1773 that the highest-density lattice packing of circles is the hexagonal packing arrangement, in which the centres of the circles are arranged in a hexagonal lattice (staggered rows, like ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus
In geometry, a torus (: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanarity, coplanar with the circle. The main types of toruses include ring toruses, horn toruses, and spindle toruses. A ring torus is sometimes colloquially referred to as a donut or doughnut. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution, also known as a ring torus. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a Lemon (geometry), spindle torus (or ''self-crossing torus'' or ''self-intersecting torus''). If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a ''toroid'', as in a square toroid. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microsoft PowerPoint
Microsoft PowerPoint is a presentation program, developed by Microsoft. It was originally created by Robert Gaskins, Tom Rudkin, and Dennis Austin at a software company named Forethought, Inc. It was released on April 20, 1987, initially for Macintosh computers only. Microsoft acquired PowerPoint for about $14 million three months after it appeared. This was Microsoft's first significant acquisition, and Microsoft set up a new business unit for PowerPoint in Silicon Valley where Forethought had been located. PowerPoint became a component of the Microsoft Office suite, first offered in 1989 for Macintosh and in 1990 for Microsoft Windows, Windows, which bundled several Microsoft apps. Beginning with PowerPoint 4.0 (1994), PowerPoint was integrated into Microsoft Office development, and adopted shared common components and a converged user interface. PowerPoint's market share was very small at first, prior to introducing a version for Microsoft Windows, but grew rapidly wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roya Zandi
Roya Zandi is an American physicist whose research involves the self-assembly of the viruses and fluctuation-induced or Casimir forces. She is a professor of physics and astronomy at the University of California, Riverside, and the director of the university's biophysics graduate program. Education and career Zandi studied physics at California State University, Northridge, graduating summa cum laude in 1992 and continuing for a master's degree in 1994.. She went to the University of California, Los Angeles (UCLA) for doctoral study in physics, completing her Ph.D. in 2001. Her dissertation, ''Nucleosomes and Polyelectrolytes'', was supervised by Joseph Rudnick. After postdoctoral research at UCLA and the Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The Royal Society A
''Proceedings of the Royal Society'' is the main research journal of the Royal Society. The journal began in 1831 and was split into two series in 1905: * Series A: for papers in physical sciences and mathematics. * Series B: for papers in life sciences. Many landmark scientific discoveries are published in the Proceedings, making it one of the most important science journals in history. The journal contains several articles written by prominent scientists such as Paul Dirac, Werner Heisenberg, Ernest Rutherford, Erwin Schrödinger, William Lawrence Bragg, Lord Kelvin, J.J. Thomson, James Clerk Maxwell, Dorothy Hodgkin and Stephen Hawking. In 2004, the Royal Society began '' The Journal of the Royal Society Interface'' for papers at the interface of physical sciences and life sciences. History The journal began in 1831 as a compilation of abstracts of papers in the '' Philosophical Transactions of the Royal Society'', the older Royal Society publication, that began in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kissing Number Problem
In geometry, the kissing number of a mathematical space is defined as the greatest number of non-overlapping unit spheres that can be arranged in that space such that they each touch a common unit sphere. For a given sphere packing (arrangement of spheres) in a given space, a kissing number can also be defined for each individual sphere as the number of spheres it touches. For a Lattice (group), lattice packing the kissing number is the same for every sphere, but for an arbitrary sphere packing the kissing number may vary from one sphere to another. Other names for kissing number that have been used are Newton number (after the originator of the problem), and contact number. In general, the kissing number problem seeks the maximum possible kissing number for n-sphere, ''n''-dimensional spheres in (''n'' + 1)-dimensional Euclidean space. Ordinary spheres correspond to two-dimensional closed surfaces in three-dimensional space. Finding the kissing number when centers of spheres a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Code
In geometry and coding theory, a spherical code with parameters (''n'',''N'',''t'') is a set of ''N'' points on the unit hypersphere in ''n'' dimensions for which the dot product of unit vectors from the origin to any two points is less than or equal to ''t''. The kissing number problem may be stated as the problem of finding the maximal ''N'' for a given ''n'' for which a spherical code with parameters (''n'',''N'',1/2) exists. The Tammes problem In geometry, the Tammes problem is a problem in circle packing, packing a given number of points on the surface of a sphere such that the minimum distance between points is maximized. It is named after the Dutch botanist Pieter Merkus Lambertus ... may be stated as the problem of finding a spherical code with minimal ''t'' for given ''n'' and ''N''. External links *A library of putatively optimal spherical codes Coding theory {{Geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coral Sphere Flynn Reef
Corals are colonial marine invertebrates within the subphylum Anthozoa of the phylum Cnidaria. They typically form compact colonies of many identical individual polyps. Coral species include the important reef builders that inhabit tropical oceans and secrete calcium carbonate to form a hard skeleton. A coral "group" is a colony of very many genetically identical polyps. Each polyp is a sac-like animal typically only a few millimeters in diameter and a few centimeters in height. A set of tentacles surround a central mouth opening. Each polyp excretes an exoskeleton near the base. Over many generations, the colony thus creates a skeleton characteristic of the species which can measure up to several meters in size. Individual colonies grow by asexual reproduction of polyps. Corals also breed sexually by spawning: polyps of the same species release gametes simultaneously overnight, often around a full moon. Fertilized eggs form planulae, a mobile early form of the coral polyp whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
