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Honeycombs (geometry)
A honeycomb is a mass of Triangular prismatic honeycomb#Hexagonal prismatic honeycomb, hexagonal prismatic cells built from beeswax by honey bees in their beehive, nests to contain their brood (eggs, larvae, and pupae) and stores of honey and pollen. beekeeping, 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 honey extractor. If the honeycomb is too worn out, the wax can be reused in a number of ways, including making sheets of comb Wax foundation, foundation with a hexagonal pattern. Such foundation sheets allow the bees to build the comb with less effort, and the hexagonal pattern of Worker bee, worker-sized cell bases discourages the bees from building the larger Drone (bee), drone c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Queen Excluder
In beekeeping, a queen excluder is a selective barrier inside the beehive that allows worker bees but not the larger queens and drones to traverse the barrier. The bars have a distance of 4.2 millimeters. The barrier grid was probably invented around 1890. The purpose is to prevent the queen from moving from the brood chamber to the honey chamber. There she would lay her eggs between storage cells with honey, so that bee larvae or eggs would get into the honey during centrifuging. Queen excluders are also used with some queen breeding methods. Design Typically, the queen excluder is either a sheet of perforated metal or plastic or a wire grid in a frame with openings are limited to . Queen excluders can also be constructed of hardware cloth screen, of which #5 hardware cloth is often cited in references as sufficient for allowing worker bees to pass, but not queens. Purpose The intent of the queen excluder is to limit the queen's access to the honey supers. If the qu ... [...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 Paolo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume
Volume is a measure of regions in 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 and height (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. By metonymy, the term "volume" sometimes is used to refer to the corresponding region (e.g., bounding volume). In ancient times, volume was measured using similar-shaped natural containers. Later on, standardized containers were used. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape ... [...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, the honeycomb conjecture, and the dodecahedral 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 with a dissertation 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Brożek
Jan Brożek or Johannes Broscius (November 1585 – 21 November 1652) was the most prominent Polish mathematician of his era and an early biographer of Copernicus. He held numerous ecclesiastical offices in the Catholic Church and was associated with the Kraków Academy for his entire career. Life Brożek was born in Kurzelów, a village in south-central Poland. His father, Jakub, was an educated landowner who introduced Jan to the principles of geometry. He received his primary education in Kurzelow, then continued his education in Krakow. In 1604, he enrolled in the Kraków Academy (now Jagiellonian University), where he received his baccalaureate on 30 March 1605. In 1610, he earned a magister degree (equivalent to a doctorate). His association with the Belgian mathematician, Adriaan van Roomen, greatly influenced his studies. In early 1614, Brożek was appointed professor of astrology at the Kraków Academy. In 1618 he travelled to Torun, Danzig and Frombork gathering mate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Honeycomb Theorem
The honeycomb theorem, formerly 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 ... [...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] |
Perimeter
A perimeter is the length of a closed boundary that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional line. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Tiling
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of or (as a Truncation (geometry), truncated triangular tiling). English mathematician John Horton Conway, John Conway called it a hextille. The internal angle of the hexagon is 120 degrees, so three hexagons at a point make a full 360 degrees. It is one of List of regular polytopes#Euclidean tilings, three regular tilings of the plane. The other two are the triangular tiling and the square tiling. Structure and properties The hexagonal tiling has a structure consisting of a regular hexagon only as its prototile, sharing two vertices with other identical ones, an example of monohedral tiling. Each vertex at the tiling is surrounded by three regular hexagons, denoted as 6.6.6 by vertex configuration. The dual of a hexagonal tiling is triangular tiling, because the center of each hexagonal tiling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slope
In mathematics, the slope or gradient of a Line (mathematics), line is a number that describes the direction (geometry), direction of the line on a plane (geometry), plane. Often denoted by the letter ''m'', slope is calculated as the ratio of the vertical change to the horizontal change ("rise over run") between two distinct points on the line, giving the same number for any choice of points. The line may be physical – as set by a Surveying, road surveyor, pictorial as in a diagram of a road or roof, or Pure mathematics, abstract. An application of the mathematical concept is found in the grade (slope), grade or gradient in geography and civil engineering. The ''steepness'', incline, or grade of a line is the absolute value of its slope: greater absolute value indicates a steeper line. The line trend is defined as follows: *An "increasing" or "ascending" line goes from left to right and has positive slope: m>0. *A "decreasing" or "descending" line goes from left to right ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brachygastra Mellifica
''Brachygastra mellifica'', commonly known as the Mexican honey wasp, is a neotropical social wasp. It can be found in North America. ''B. mellifica'' is one of few wasp species that produces honey. It is also considered a delicacy in some cultures in Mexico. This wasp species is of use to humans because it can be used to control pest species and to pollinate avocados. Taxonomy and phylogeny The species that comprise the genus '' Brachygastra'' are neotropical social wasps. They can be found from southern United States to Northern Argentina and include a total of 16 species. ''B. mellifica'' is the only species present in the US, found in both Arizona and Texas. ''B. mellifica'' ranges from Texas to Panama. This genus is known for its easily recognizable abdomen, which can be almost as wide as it is long, and its very high scutellum that often projects over the metanotum. ''B. mellifica'' is very similar in morphology to '' B. lecheguana'' but differs in its geographic distrib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
