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Fat Object
In geometry, a fat object is an object in two or more dimensions, whose lengths in the different dimensions are similar. For example, a square is fat because its length and width are identical. A 2-by-1 rectangle is thinner than a square, but it is fat relative to a 10-by-1 rectangle. Similarly, a circle is fatter than a 1-by-10 ellipse and an equilateral triangle is fatter than a very obtuse triangle. Fat objects are especially important in computational geometry. Many algorithms in computational geometry can perform much better if their input consists of only fat objects; see the applications section below.
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  • 28 Nov 2022
Topic Review
Magnoliophyta
Flowering plants are plants that bear flowers and fruits, and form the clade Angiospermae (/ˌændʒiəˈspɜːrmiː/), commonly called angiosperms. The term "angiosperm" is derived from the Greek words angeion ('container, vessel') and sperma ('seed'), and refers to those plants that produce their seeds enclosed within a fruit. They are by far the most diverse group of land plants with 64 orders, 416 families, approximately 13,000 known genera and 300,000 known species. Angiosperms were formerly called Magnoliophyta (/mæɡˌnoʊliˈɒfətə, -əˈfaɪtə/). Like gymnosperms, angiosperms are seed-producing plants. They are distinguished from gymnosperms by characteristics including flowers, endosperm within their seeds, and the production of fruits that contain the seeds. The ancestors of flowering plants diverged from the common ancestor of all living gymnosperms before the end of the Carboniferous, over 300 million years ago. The closest fossil relatives of flowering plants are uncertain and contentious. The earliest angiosperm fossils are in the form of pollen around 134 million years ago during the Early Cretaceous. Over the course of the Cretaceous, angiosperms explosively diversified, becoming the dominant group of plants across the planet by the end of the period, corresponding with the decline and extinction of previously widespread gymnosperm groups. The origin and diversification of the angiosperms is often known as "Darwin's abominable mystery".
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Topic Review
Petr–Douglas–Neumann Theorem
In geometry, the Petr–Douglas–Neumann theorem (or the PDN-theorem) is a result concerning arbitrary planar polygons. The theorem asserts that a certain procedure when applied to an arbitrary polygon always yields a regular polygon having the same number of sides as the initial polygon. The theorem was first published by Karel Petr (1868–1950) of Prague in 1908. The theorem was independently rediscovered by Jesse Douglas (1897–1965) in 1940 and also by B H Neumann (1909–2002) in 1941. The naming of the theorem as Petr–Douglas–Neumann theorem, or as the PDN-theorem for short, is due to Stephen B Gray. This theorem has also been called Douglas's theorem, the Douglas–Neumann theorem, the Napoleon–Douglas–Neumann theorem and Petr's theorem. The PDN-theorem is a generalisation of the Napoleon's theorem which is concerned about arbitrary triangles and of the van Aubel's theorem which is related to arbitrary quadrilaterals.
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Topic Review
Scholarly Interpretation of Gospel-Elements
Scholars have given various interpretations of the elements of the Gospel-stories.
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Topic Review
Stadt Huys Site
The Stadt Huys (an old Dutch spelling, meaning city hall) was the very first city hall in New York City built in 17th-century during Dutch settlement (New Amsterdam). It stopped function in 1679 due to safety. It is located at the 71 Pearl Street today. The Stadt Huys block archaeology project was the first large scale archaeological excavation in New York City in 1979-1980. At the time it was excavated, it was one of the most expensive and most productive projects of urban archeology undertaken in an American city. A lot of logistical procedures for urban archaeology had to be developed as the project evolved. Most of these procedures have become a model for performing large-scale excavations in the city.
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Topic Review
Risk Factors of Schizophrenia
Risk factors of schizophrenia include multiple genetic and environmental risk factors. The prevailing model of schizophrenia is that of a neurodevelopmental disorder with no precise boundary, or single cause, and is thought to develop from complex gene–environment interactions with involved vulnerability factors. The interactions of these risk factors are complicated, as numerous and diverse insults from conception to adulthood can be involved. The combination of genetic and environmental factors leads to deficits in the neural circuits that affect sensory input and cognitive functions. A genetic predisposition on its own, without interacting environmental factors, will not give rise to the development of schizophrenia. Environmental risk factors are many, and include pregnancy complications, prenatal stress and nutrition, and adverse childhood experiences. An environmental risk factor may act alone or in combination with others. Schizophrenia typically develops between the ages of 16–30 (generally males aged 16–25 years and females 25–30 years); about 75 percent of people living with the illness developed it in these age-ranges. Childhood schizophrenia that develops before the age of 13 is quite rare. There is on average a somewhat earlier onset for men than women, with the possible influence of the female sex hormone estrogen being one hypothesis and socio-cultural influences another. Estrogen is seen to have a dampening effect on dopamine receptors.
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Topic Review
AFVG
AFVG (standing for Anglo-French Variable Geometry) was a 1960s project for supersonic multi-role combat aircraft with a variable-geometry wing,[N 1] jointly developed by British Aircraft Corporation in the United Kingdom and Dassault Aviation of France. The project was borne out of ambitions to produce a viable combat aircraft that made use of the variable-sweep wing, as well as to promote wider cooperative efforts between France and the United Kingdom. However, neither Dassault not the French Air Force were particularly keen on the AFVG; the project was further impacted by repeated specification changes and indecision for what roles that the AFVG was to be tasked with on the part of Britain. In mid-1967, British requirements settled upon adopting the AFVG for the Royal Air Force (RAF) for the strike role in the place of the cancelled BAC TSR-2 strike bomber. The project was cancelled in June 1967, when the French Government withdrew from participation. However, the cancellation was not the end of work on the proposed design. BAC modified the specification to solely satisfy Royal Air Force (RAF) needs, reconfiguring the design as the UKVG and sought out new partners to procure the aircraft, which ultimately emerged as the Anglo-German-Italian consortium-funded MRCA (Panavia Tornado), a variable-geometry wing fighter/strike aircraft.
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Topic Review
Inclusive Fitness
In evolutionary biology, inclusive fitness is one of two metrics of evolutionary success as defined by W. D. Hamilton in 1964. An individual's own child, who carries one half of the individual's genes, is defined as one offspring equivalent. A sibling's child, who will carry one-quarter of the individual's genes, is 1/2 offspring equivalent. Similarly, a cousin's child, who has 1/16 of the individual's genes, is 1/8 offspring equivalent. From the gene's point of view, evolutionary success ultimately depends on leaving behind the maximum number of copies of itself in the population. Prior to Hamilton's work, it was generally assumed that genes only achieved this through the number of viable offspring produced by the individual organism they occupied. However, this overlooked a wider consideration of a gene's success, most clearly in the case of the social insects where the vast majority of individuals do not produce (their own) offspring.
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Topic Review
Capital Centre
The Capital Centre (later USAir Arena and US Airways Arena) was an indoor arena in the eastern United States, located in Landover, Maryland, east of Washington, D.C. Opened in late 1973, it closed in 1999, and was demolished in 2002. The seating capacity was 18,756 for basketball and 18,130 for hockey. The elevation at street level was approximately 160 feet (50 m) above sea level. The U.S. Census Bureau defined the land, later occupied by The Boulevard at the Capital Centre, as being in the Mitchellville census-designated place as of the 1990 U.S. Census, while in the 2000 U.S. Census the area was placed in the Lake Arbor CDP.
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Topic Review
Fault (Legal)
Fault, as a legal term, refers to legal blameworthiness and responsibility in each area of law. It refers to both the actus reus and the mental state of the defendant. The basic principle is that a defendant should be able to contemplate the harm that his actions may cause, and therefore should aim to avoid such actions. Different forms of liability employ different notions of fault, in some there is no need to prove fault, but the absence of it. In criminal law, the mens rea is used to decide if the defendant has criminal intent when he commits the act and, if so, he is therefore liable for the crime. However, this is not necessary for strict liability offences, where no particular state of mind is required to satisfy the burden of proof.
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