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Paper Bag Problem
In geometry, the paper bag problem or teabag problem is to calculate the maximum possible inflated volume of an initially flat sealed rectangular bag which has the same shape as a cushion or pillow, made out of two pieces of material which can bend but not stretch. According to Anthony C. Robin, an approximate formula for the capacity of a sealed expanded bag is: :V=w^3 \left (h/ \left (\pi w \right ) -0.142 \left (1-10^ \left (-h/w \right ) \right ) \right ), where ''w'' is the width of the bag (the shorter dimension), ''h'' is the height (the longer dimension), and ''V'' is the maximum volume. The approximation ignores the crimping round the equator of the bag. A very rough approximation to the capacity of a bag that is open at one edge is: :V=w^3 \left (h/ \left (\pi w \right ) -0.071 \left (1-10^ \left (-2h/w \right ) \right ) \right ) (This latter formula assumes that the corners at the bottom of the bag are linked by a single edge, and that the base of the bag is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Cushion
A cushion is a soft bag of some ornamental material, usually stuffed with wool, hair, feathers, polyester staple fiber, non-woven material, cotton, or even paper torn into fragments. It may be used for sitting or kneeling upon, or to soften the hardness or angularity of a chair or couch. Decorative cushions often have a patterned cover material, and are used as decoration for furniture. A cushion is also referred to as a bolster, hassock, ''headrest'', a ''tush'', and a ''sham''. Cushions and rugs can be used temporarily outside to soften a hard ground. They can be placed on sunloungers and used to prevent annoyances from moist grass and biting insects. Some dialects of English use this word to refer to throw pillows as well. The cushion is a very ancient article of furniture; the inventories of the contents of palaces and great houses in the early Middle Ages constantly made mention of them. Cushions were then often of great size, covered with leather, and firm enough ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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] [Amazon] |
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Cushion
A cushion is a soft bag of some ornamental material, usually stuffed with wool, hair, feathers, polyester staple fiber, non-woven material, cotton, or even paper torn into fragments. It may be used for sitting or kneeling upon, or to soften the hardness or angularity of a chair or couch. Decorative cushions often have a patterned cover material, and are used as decoration for furniture. A cushion is also referred to as a bolster, hassock, ''headrest'', a ''tush'', and a ''sham''. Cushions and rugs can be used temporarily outside to soften a hard ground. They can be placed on sunloungers and used to prevent annoyances from moist grass and biting insects. Some dialects of English use this word to refer to throw pillows as well. The cushion is a very ancient article of furniture; the inventories of the contents of palaces and great houses in the early Middle Ages constantly made mention of them. Cushions were then often of great size, covered with leather, and firm enough ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Pillow
A pillow is a support of the body at rest for comfort, therapy, or decoration. Pillows are used in different variations by many species, including humans. Some types of pillows include throw pillows, body pillows, decorative pillows, and many more. Pillows that aid sleeping are a form of bedding that supports the head and neck. Other types of pillows are designed to support the body when lying down or sitting. There are also pillows that consider human body shape for increased comfort during sleep. Decorative pillows used on beds, couches or chairs are sometimes referred to as cushions. In contemporary western culture, pillows consist of a plain or patterned fabric envelope (known as a pillowcase) which contains a soft stuffing, typically synthetic and typically standardized in sizes and shape. Pillows have been historically made of a variety of natural materials and many cultures continue to use pillows made from natural materials in the world. The word ''pillow'' comes fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Lens (geometry)
In 2-dimensional geometry, a lens is a convex set, convex region bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both arcs must bow outwards (convex-convex). This shape can be formed as the intersection of two disk (mathematics), circular disks. It can also be formed as the union of two circular segments (regions between the Chord (geometry), chord of a circle and the circle itself), joined along a common chord. Types If the two arcs of a lens have equal radius, it is called a symmetric lens, otherwise is an asymmetric lens. The vesica piscis is one form of a symmetric lens, formed by arcs of two circles whose centers each lie on the opposite arc. The arcs meet at angles of 120° at their endpoints. Area ;Symmetric The area of a symmetric lens can be expressed in terms of the radius ''R'' and arc lengths ''θ'' in radians: :A = R^2\left(\theta - \sin \theta \right). ;Asymmetric The area of an asymmetric lens f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Teabag
A tea bag (or teabag) is a small, porous, sealed bag or packet typically containing tea leaves (''Camellia sinensis'') or the leaves of other herbs, which is immersed in water to steep and make an infusion. Originally used only for making tea, they are now made for other tisanes (herbal "teas") as well. Tea bags are commonly made of filter paper or food-grade plastic, or occasionally of silk cotton or silk. The tea bag performs the same function as a tea infuser. Tea bags can be used multiple times until there is no extraction left. Some tea bags have an attached piece of string with a paper label at the top that assists in removing the bag, while also displaying the brand or variety of tea. There are also special tea filters that can be used to pour loose tea into and brew it in a bag in a cup. History Tea bag patents date from 1903, when Roberta Lawson and Mary McLaren, of Milwaukee, Wisconsin, were granted US patent 723287 for a Tea Leaf Holder, which they had filed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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University Of Newcastle, Australia
The University of Newcastle is a Public university#Australia, public university in Newcastle, New South Wales, Australia. Established in 1965, it has a primary campus in the Newcastle suburb of Callaghan, New South Wales, Callaghan. The university also operates campuses in Central Coast, New South Wales, Central Coast, Singapore, Newcastle, New South Wales, Newcastle City in the Hunter Region, Hunter as well as Sydney. The University of Newcastle is a member of the Australian Technology Network, Universities Australia and the Association to Advance Collegiate Schools of Business. History Establishment The earliest origins of the present-day University of Newcastle can be traced to the Newcastle Teachers College (established 1949) and Newcastle University College (NUC, established 1951). NUC was created as an offshoot of the New South Wales University of Technology (now known as the University of New South Wales) and was co-located with the Newcastle Technical College at Tig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Biscornu
A biscornu is a small, octagonal, stuffed ornamental pincushion. It is usually made out of Aida cloth or linen, sewn from two square sheets of cloth (forming the top and bottom of the cushion) in such a way that each corner of one square is hemmed to the middle of a side of the opposite square. The term "biscornu" comes from the French adjective ''biscornu'', which means irregular, skewed, or odd. Embroidery, hardanger, and/or cross-stitch are used to decorate the top and bottom of the cushion. A button is typically secured in the center of the cushion to give a small depression on the top. Beads, tassels and other objects can decorate the biscornu. They are typically able to fit in the palm of your hand. The name is derived from the French adjective, '' biscornu'', meaning skewed, quirky or irregular. Mathematically, two squares joined together in the pattern of a biscornu will form the boundary of a unique convex polyhedron, by Alexandrov's uniqueness theorem.. In the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Mylar Balloon (geometry)
BoPET (biaxially oriented polyethylene terephthalate) is a polyester film made from stretched polyethylene terephthalate (PET) and is used for its high tensile strength, chemical stability, dimensional stability, transparency reflectivity, and electrical insulation. When metallized, it has gas and moisture barrier properties. The film is "biaxially oriented", which means that the polymer chains are oriented parallel to the plane of the film, and therefore oriented over two axes. A variety of companies manufacture boPET and other polyester films under different brand names. In the UK and US, the best-known trade names are Mylar, Melinex, Lumirror and Hostaphan. It was the first biaxially oriented polymer to be manufactured on a mass commercial scale. History BoPET film was developed in the mid-1950s,Izard, Emmette Farr"Production of polyethylene terephthalate" U.S. patent no. 2,534,028 (filed: 1948 May 13; issued: 1950 December 12). originally by DuPont, Imperial Chemical In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Institute Of Mathematics And Its Applications
The Institute of Mathematics and its Applications (IMA) is the UK's chartered professional body for mathematicians and one of the UK's learned societies for mathematics (another being the London Mathematical Society). The IMA aims to advance mathematics and its applications, promote and foster research and other enquiries directed the advancement, teaching and application of mathematics, to seek to establish and maintain high standards of professional conduct for members and to seek to promote, encourage and guide the development of education and training in mathematics.Listing Charity Commission History In 1959, the need for a professional and learned body for mat ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign. History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled ''CRC Concise Encyclopedia of Mathematics''. The free online version became only partially accessible to the public. In 1999 Weisstein we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Geometric Shapes
A shape is a graphics, graphical representation of an object's form or its external boundary, outline, or external Surface (mathematics), surface. It is distinct from other object properties, such as color, Surface texture, texture, or material type. In geometry, ''shape'' excludes information about the object's Position (geometry), position, size, Orientation (geometry), orientation and chirality. A ''figure'' is a representation including both shape and size (as in, e.g., figure of the Earth). A plane shape or plane figure is constrained to lie on a ''plane (geometry), plane'', in contrast to ''solid figure, solid'' 3D shapes. A two-dimensional shape or two-dimensional figure (also: 2D shape or 2D figure) may lie on a more general curved ''surface (mathematics), surface'' (a two-dimensional space). Classification of simple shapes Some simple shapes can be put into broad categories. For instance, polygons are classified according to their number of edges as triangles, qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |