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Faveolate
A honeycomb is a mass of hexagonal prismatic wax cells built by honey bees in their nests to contain their larvae and stores of honey and pollen. Beekeepers may remove the entire honeycomb to harvest honey. Honey bees consume about of honey to secrete of wax, and so beekeepers may return the wax to the hive after harvesting the honey to improve honey outputs. The structure of the comb may be left basically intact when honey is extracted from it by uncapping and spinning in a centrifugal machine, more specifically a honey extractor. If the honeycomb is too worn out, the wax can be reused in a number of ways, including making sheets of comb foundation with hexagonal pattern. Such foundation sheets allow the bees to build the comb with less effort, and the hexagonal pattern of worker-sized cell bases discourages the bees from building the larger drone cells. Fresh, new comb is sometimes sold and used intact as comb honey, especially if the honey is being spread on bread rather t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Honeycombs For Sale - Saraeyn - Iranian Azerbaijan - Iran (7421128352)
A honeycomb is a mass of hexagonal prismatic wax cells built by honey bees in their nests to contain their larvae and stores of honey and pollen. Beekeepers may remove the entire honeycomb to harvest honey. Honey bees consume about of honey to secrete of wax, and so beekeepers may return the wax to the hive after harvesting the honey to improve honey outputs. The structure of the comb may be left basically intact when honey is extracted from it by uncapping and spinning in a centrifugal machine, more specifically a honey extractor. If the honeycomb is too worn out, the wax can be reused in a number of ways, including making sheets of comb foundation with hexagonal pattern. Such foundation sheets allow the bees to build the comb with less effort, and the hexagonal pattern of worker-sized cell bases discourages the bees from building the larger drone cells. Fresh, new comb is sometimes sold and used intact as comb honey, especially if the honey is being spread on bread rather t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polistinae
The Polistinae is a subfamily of eusocial wasps belonging to the Family (biology), family Vespidae. They are closely related to the more familiar wasps (“yellowjackets” as they are called in North America) and true hornets of the subfamily Vespinae, containing four tribes. With about 1,100 species total, it is the second-most diverse subfamily within the Vespidae, and while most species are tropical or subtropical, they include some of the most frequently encountered large wasps in temperate regions. The Polistinae are also known as paper wasps, which is a misleading term, since other wasps (including the wasps in the subfamily Vespinae) also build nests out of paper, and because some epiponine wasps (e.g., ''Polybia emaciata'') build theirs out of mud, nonetheless, the name "paper wasp" seems to apply mostly, but not exclusively, to the Polistinae, especially the Polistini. Many polistines, such as ''Polistes fuscatus,'' ''Polistes annularis'', and ''Polistes exclamans'', m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
On Growth And Form
''On Growth and Form'' is a book by the Scottish mathematical biologist D'Arcy Wentworth Thompson (1860–1948). The book is long – 793 pages in the first edition of 1917, 1116 pages in the second edition of 1942. The book covers many topics including the effects of scale on the shape of animals and plants, large ones necessarily being relatively thick in shape; the effects of surface tension in shaping soap films and similar structures such as cells; the logarithmic spiral as seen in mollusc shells and ruminant horns; the arrangement of leaves and other plant parts (phyllotaxis); and Thompson's own method of transformations, showing the changes in shape of animal skulls and other structures on a Cartesian grid. The work is widely admired by biologists, anthropologists and architects among others, but less often read than cited. Peter Medawar explains this as being because it clearly pioneered the use of mathematics in biology, and helped to defeat mystical ideas of vitali ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soap Bubble
A soap bubble is an extremely thin film of soap or detergent and water enclosing air that forms a hollow sphere with an iridescent surface. Soap bubbles usually last for only a few seconds before bursting, either on their own or on contact with another object. They are often used for children's enjoyment, but they are also used in artistic performances. Assembling many bubbles results in foam. When light shines onto a bubble it appears to change colour. Unlike those seen in a rainbow, which arise from differential refraction, the colours seen in a soap bubble arise from light wave interference, reflecting off the front and back surfaces of the thin soap film. Depending on the thickness of the film, different colours interfere constructively and destructively. Mathematics Soap bubbles are physical examples of the complex mathematical problem of minimal surface. They will assume the shape of least surface area possible containing a given volume. A true minimal surface is more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Arcy Wentworth Thompson
Sir D'Arcy Wentworth Thompson CB FRS FRSE (2 May 1860 – 21 June 1948) was a Scottish biologist, mathematician and classics scholar. He was a pioneer of mathematical and theoretical biology, travelled on expeditions to the Bering Strait and held the position of Professor of Natural History at University College, Dundee for 32 years, then at St Andrews for 31 years. He was elected a Fellow of the Royal Society, was knighted, and received the Darwin Medal and the Daniel Giraud Elliot Medal. Thompson is remembered as the author of the 1917 book ''On Growth and Form'', which led the way for the scientific explanation of morphogenesis, the process by which patterns and body structures are formed in plants and animals. Thompson's description of the mathematical beauty of nature, and the mathematical basis of the forms of animals and plants, stimulated thinkers as diverse as Julian Huxley, C. H. Waddington, Alan Turing, René Thom, Claude Lévi-Strauss, Eduardo Paolozzi, Le Co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length (cubed) is interrelated with volume. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. In ancient times, volume is measured using similar-shaped natural containers and later on, standardized containers. Some simple three-dimensional shapes can have its volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. Zero-, one- and two-dimensional objects have no volume; in fourth and higher dimensions, an analogous concept to the normal vo ... [...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] |
Jan Brożek
Jan Brożek (''Ioannes Broscius'', ''Joannes Broscius'' or ''Johannes Broscius''; 1 November 1585 – 21 November 1652) was a Polish polymath: a mathematician, astronomer, physician, poet, writer, musician and rector of the Kraków Academy. Life Brożek was born in Kurzelów, Sandomierz Province, and lived in Kraków, Staszów, and Międzyrzec Podlaski. He received his primary education in Kurzelow, then continued education in Krakow. In 1604, he enrolled in the Faculty of Liberal Art at the Kraków Academy (now Jagiellonian University), where he received his baccalaureate on 30 March 1605. In January 1614, he became the head of the Astronomy and Astrology Faculty. From 1620 to 1624, he stayed in Padua, where he studied medicine at the University of Padua and received his doctorate in medicine on 11 August 1623. He served as rector of Jagiellonian University. He was the most prominent Polish mathematician of the 17th century, working on the theory of numbers (particularly perf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Honeycomb Conjecture
The honeycomb conjecture states that a regular hexagonal grid or honeycomb has the least total perimeter of any subdivision of the plane into regions of equal area. The conjecture was proven in 1999 by mathematician Thomas C. Hales. Theorem Let \Gamma be any system of smooth curves in \mathbb^2, subdividing the plane into regions (connected components of the complement of \Gamma) all of which are bounded and have unit area. Then, averaged over large disks in the plane, the average length of \Gamma per unit area is at least as large as for the hexagon tiling. The theorem applies even if the complement of \Gamma has additional components that are unbounded or whose area is not one; allowing these additional components cannot shorten \Gamma. Formally, let B(0,r) denote the disk of radius r centered at the origin, let L_r denote the total length of \Gamma\cap B(0,r), and let A_r denote the total area of B(0,r) covered by bounded unit-area components. (If these are the only components, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perimeter
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter; if the length of the string was exact, it would equal the perimeter. Formulas The perimeter is the distance around a shape. Perimeters for more general shapes can be calculated, as any path, with \int_0^L \mathrms, where L is the length of the path and ds is an infinitesimal line element. Both of these must be replaced by algebraic forms in order to be practically calculated. If the perimeter is given as a closed piecewise smooth plane curve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional spaces, higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include ''regular tilings'' with regular polygonal tiles all of the same shape, and ''semiregular tilings'' with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An ''aperiodic tiling'' uses a small set of tile shapes that cannot form a repeating pattern. A ''tessellation of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
