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Topic Review
Sierpinski Triangle
The Sierpinski triangle (also with the original orthography Sierpiński), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self-similar sets, i.e., it is a mathematically generated pattern that is reproducible at any magnification or reduction. It is named after the Poland mathematician Wacław Sierpiński, but appeared as a decorative pattern many centuries before the work of Sierpiński.
  • 12.4K
  • 04 Nov 2022
Topic Review
Cyclic Quadrilateral
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. The center of the circle and its radius are called the circumcenter and the circumradius respectively. Other names for these quadrilaterals are concyclic quadrilateral and chordal quadrilateral, the latter since the sides of the quadrilateral are chords of the circumcircle. Usually the quadrilateral is assumed to be convex, but there are also crossed cyclic quadrilaterals. The formulas and properties given below are valid in the convex case. The word cyclic is from the Ancient Greek κύκλος (kuklos) which means "circle" or "wheel". All triangles have a circumcircle, but not all quadrilaterals do. An example of a quadrilateral that cannot be cyclic is a non-square rhombus. The section characterizations below states what necessary and sufficient conditions a quadrilateral must satisfy to have a circumcircle.
  • 12.2K
  • 27 Oct 2022
Topic Review
Digital Twin: Origin to Future
Digital Twin (DT) refers to the virtual copy or model of any physical entity (physical twin) both of which are interconnected via exchange of data in real time. Conceptually, a DT mimics the state of its physical twin in real time and vice versa. Application of DT includes real-time monitoring, designing/planning, optimization, maintenance, remote access, etc. Its implementation is expected to grow exponentially in the coming decades. The advent of Industry 4.0 has brought complex industrial systems that are more autonomous, smart, and highly interconnected. These systems generate considerable amounts of data useful for several applications such as improving performance, predictive maintenance, training, etc. A sudden influx in the number of publications related to ‘Digital Twin’ has led to confusion between different terminologies related to the digitalization of industries. Another problem that has arisen due to the growing popularity of DT is a lack of consensus on the description of DT as well as so many different types of DT, which adds to the confusion. This paper intends to consolidate the different types of DT and different definitions of DT throughout the literature for easy identification of DT from the rest of the complimentary terms such as ‘product avatar’, ‘digital thread’, ‘digital model’, and ‘digital shadow’. The paper looks at the concept of DT since its inception to its predicted future to realize the value it can bring to certain sectors. Understanding the characteristics and types of DT while weighing its pros and cons is essential for any researcher, business, or sector before investing in the technology.
  • 12.0K
  • 25 Jun 2021
Topic Review
Partition (Number Theory)
In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.) For example, 4 can be partitioned in five distinct ways: 4 3 + 1 2 + 2 2 + 1 + 1 1 + 1 + 1 + 1 The order-dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same partition 2 + 1 + 1. A summand in a partition is also called a part. The number of partitions of n is given by the partition function p(n). So p(4) = 5. The notation λ ⊢ n means that λ is a partition of n. Partitions can be graphically visualized with Young diagrams or Ferrers diagrams. They occur in a number of branches of mathematics and physics, including the study of symmetric polynomials and of the symmetric group and in group representation theory in general.
  • 11.7K
  • 04 Nov 2022
Topic Review
News International Phone Hacking Scandal
The News International phone hacking scandal was a controversy involving the now-defunct News of the World and other British newspapers owned by Rupert Murdoch. Employees of the newspaper were accused of engaging in phone hacking, police bribery, and exercising improper influence in the pursuit of stories. Whilst investigations conducted from 2005 to 2007 appeared to show that the paper's phone hacking activities were limited to celebrities, politicians, and members of the British royal family, in July 2011 it was revealed that the phones of murdered schoolgirl Milly Dowler, relatives of deceased British soldiers, and victims of the 7 July 2005 London bombings had also been hacked. The resulting public outcry against News Corporation and its owner Rupert Murdoch led to several high-profile resignations, including that of Murdoch as News Corporation director, Murdoch's son James as executive chairman, Dow Jones chief executive Les Hinton, News International legal manager Tom Crone, and chief executive Rebekah Brooks. The commissioner of London's Metropolitan Police Service (MPS), Sir Paul Stephenson, also resigned. Advertiser boycotts led to the closure of the News of the World on 10 July 2011, after 168 years of publication. Public pressure forced News Corporation to cancel its proposed takeover of the British satellite broadcaster BSkyB. The prime minister David Cameron announced on 6 July 2011 that a public inquiry, known as the Leveson Inquiry, would look into phone hacking and police bribery by the News of the World, consider the wider culture and ethics of the British newspaper industry and that the Press Complaints Commission would be replaced "entirely". A number of arrests and convictions followed, most notably of the former News of the World managing editor Andy Coulson. Murdoch and his son, James, were summoned to give evidence at the Leveson Inquiry. Over the course of his testimony, Rupert Murdoch admitted that a cover-up had taken place within the News of the World to hide the scope of the phone hacking. On 1 May 2012, a parliamentary select committee report concluded that Murdoch "exhibited wilful blindness to what was going on in his companies and publications" and stated that he was "not a fit person to exercise the stewardship of a major international company". On 3 July 2013, Channel 4 News broadcast a secret tape in which Murdoch dismissively claims that investigators were "totally incompetent" and acted over "next to nothing" and excuses his papers' actions as "part of the culture of Fleet Street".
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  • 11 Oct 2022
Topic Review
Prince of Wales's Feathers
Template:Infobox Coat of arms The Prince of Wales's feathers is the heraldic badge of the Prince of Wales. It consists of three white ostrich feathers emerging from a gold coronet. A ribbon below the coronet bears the motto Ich dien (German: [ɪç ˈdiːn], "I serve"). As well as being used in royal heraldry, the badge is sometimes used to symbolise Wales, particularly in Welsh rugby union and Welsh regiments of the British Army.
  • 11.0K
  • 27 Nov 2022
Topic Review
Records Continuum Model
The Records Continuum Model (RCM) was created in the 1990s by Monash University academic Frank Upward with input from colleagues Sue McKemmish and Livia Iacovino as a response to evolving discussions about the challenges of managing digital records and archives in the discipline of Archival Science. The RCM was first published in Upward’s 1996 paper "Structuring the Records Continuum – Part One: Postcustodial principles and properties". Upward describes the RCM within the broad context of a continuum where activities and interactions transform documents into records, evidence and memory that are used for multiple purposes over time. Upward places the RCM within a post-custodial, postmodern and structuration conceptual framework. Australian academics and practitioners continue to explore, develop and extend the RCM and records continuum theory, along with international collaborators, via the Records Continuum Research Group (RCRG) at Monash University.
  • 10.8K
  • 09 Nov 2022
Topic Review
Hat Puzzle
Hat puzzles are logic problems that date back to as early as 1961. Such hat puzzles, frequently contextualized as prisoners and hats puzzles, are induction puzzles (a kind of logic puzzle) that involve reasoning about the actions of other people, drawing in aspects of Game theory sometimes called the hierarchy of beliefs. There are many variations, but the central theme remains the same. A number of players are each wearing a hat, which may be of various specified colours. Players can see the colours of at least some other players' hats, but not that of their own. With highly restricted communication or none, some of the players must guess the colour of their hat. The problem is to find a strategy for the players to determine the colours of their hats based on the hats they see and what the other players do. In some versions, they compete to be the first to guess correctly; in others, they can work out a strategy beforehand to cooperate and maximize the probability of correct guesses. One variation received some new publicity as a result of Todd Ebert's 1998 Ph.D. thesis at the University of California, Santa Barbara. It is a strategy question about a cooperative game, which has connections to algebraic coding theory.
  • 10.6K
  • 24 Oct 2022
Topic Review
List of International Mathematical Olympiad Participants
The International Mathematical Olympiad (IMO) is an annual international high school mathematics competition focused primarily on pre-collegiate mathematics, and is the oldest of the international science olympiads. The awards for exceptional performance include medals for roughly the top half participants, and honorable mentions for participants who solve at least one problem perfectly. This is a list of participants who have achieved notability. This includes participants that went on to become notable mathematicians, participants who won medals at an exceptionally young age, or participants who scored highly.
  • 10.4K
  • 26 Oct 2022
Topic Review
Gramian Matrix
In linear algebra, the Gram matrix (or Gramian matrix, Gramian) of a set of vectors [math]\displaystyle{ v_1,\dots, v_n }[/math] in an inner product space is the Hermitian matrix of inner products, whose entries are given by [math]\displaystyle{ G_{ij}=\langle v_i, v_j \rangle }[/math]. An important application is to compute linear independence: a set of vectors are linearly independent if and only if the Gram determinant (the determinant of the Gram matrix) is non-zero. It is named after Jørgen Pedersen Gram.
  • 10.3K
  • 27 Oct 2022
Topic Review
Quaternary Numeral System
A quaternary /kwəˈtɜːrnəri/ numeral system is base-4. It uses the digits 0, 1, 2 and 3 to represent any real number. Four is the largest number within the subitizing range and one of two numbers that is both a square and a highly composite number (the other being 36), making quaternary a convenient choice for a base at this scale. Despite being twice as large, its radix economy is equal to that of binary. However, it fares no better in the localization of prime numbers (the smallest better base being the primorial base six, senary). Quaternary shares with all fixed-radix numeral systems many properties, such as the ability to represent any real number with a canonical representation (almost unique) and the characteristics of the representations of rational numbers and irrational numbers. See decimal and binary for a discussion of these properties.
  • 9.6K
  • 16 Nov 2022
Topic Review
List of Citadel Paints
This table contains a list of the Citadel paint range used for painting Citadel Miniatures, produced by Games Workshop. Citadel Miniatures are metal, resin, and plastic miniature gaming figures, accessories, and scenery for Games Workshop's range of tabletop wargames, such as their signature Warhammer Fantasy Battle, and Warhammer 40,000 games and The Lord of the Rings Strategy Battle Game.
  • 9.6K
  • 25 Nov 2022
Topic Review
Hypothetical Construct
In philosophy, a construct is an object which is ideal, that is, an object of the mind or of thought, meaning that its existence may be said to depend upon a subject's mind. This contrasts with any possibly mind-independent objects, the existence of which purportedly does not depend on the existence of a conscious observing subject. Thus, the distinction between these two terms may be compared to that between phenomenon and noumenon in other philosophical contexts and to many of the typical definitions of the terms realism and idealism also. In the correspondence theory of truth, ideas, such as constructs, are to be judged and checked according to how well they correspond with their referents, often conceived as part of a mind-independent reality.
  • 9.5K
  • 23 Nov 2022
Topic Review
Prime Video
Prime Video, also marketed as Amazon Prime Video, is an American Internet video on demand service that is developed, owned, and operated by Amazon. It offers television shows and films for rent or purchase and Prime Video, a selection of Amazon Studios original content and licensed acquisitions included in the Amazon's Prime subscription. In the United Kingdom , United States , Germany , and many other territories, access to Prime Video is also available through a video-only membership, which does not require a full Prime subscription. In France and Italy, and other countries like Australia , Canada , India , etc. Prime Video content is only accessible through a dedicated Prime Video website. In some countries Prime Video additionally offers Amazon Channels, which allows viewers to subscribe to other suppliers' content, including HBO in the United States. Launched on September 7, 2006 as Amazon Unbox in the United States, the service grew with its expanding library, and added the Prime Video membership with the development of Prime. It was then renamed as Amazon Instant Video on Demand. After acquiring the local streaming and DVD-by-mail service LoveFilm in 2011, Prime Video was added to Prime in the United Kingdom, Germany and Austria in 2014, a move that angered some Prime UK members as the bundling was non-negotiable with a 61% increase in subscription fee. In the UK, Germany, and Austria, Prime Video has been available on a monthly subscription of £5.99 or €7.99 per month, continuing the plan of LoveFilm Instant. The service was previously available in Norway , Denmark and Sweden in 2012, but was discontinued in 2013. On April 18, 2016, Amazon split Prime Video from Amazon Prime in the US for $8.99 per month. The service also hosts Amazon Original content alongside titles on Video as well. On December 14, 2016, Prime Video launched worldwide (except for Mainland China, Cuba, Iran, North Korea, Syria) expanding its reach beyond the US, the UK, Germany, Austria, and Japan. Among the new territories, the service was included with Prime in Belgium, Canada , France , India , Italy, Spain , Poland , and Brazil , while for all other countries – for instance Bulgaria – it was made available for a monthly promotional price of $/€2.99 per month for the first six months and $/€5.99 per month thereafter.
  • 9.0K
  • 29 Nov 2022
Topic Review
Religious Studies
Religious studies, alternately known as the study of religion, is an academic field devoted to research into religious beliefs, behaviors, and institutions. It describes, compares, interprets, and explains religion, emphasizing systematic, historically based, and cross-cultural perspectives. While theology attempts to understand the nature of transcendent or supernatural forces (such as deities), religious studies tries to study religious behavior and belief from outside any particular religious viewpoint. Religious studies draws upon multiple disciplines and their methodologies including anthropology, sociology, psychology, philosophy, and history of religion. Religious studies originated in the 19th century, when scholarly and historical analysis of the Bible had flourished, and Hindu and Buddhist texts were first being translated into European languages. Early influential scholars included Friedrich Max Müller, in England, and Cornelius P. Tiele, in the Netherlands. Today religious studies is practiced by scholars worldwide. In its early years, it was known as Comparative Religion or the Science of Religion and, in the USA, there are those who today also know the field as the History of religion (associated with methodological traditions traced to the University of Chicago in general, and in particular Mircea Eliade, from the late 1950s through to the late 1980s). The term "religion" originated from the Latin noun "religio", that was nominalized from one of three verbs: "relegere" (to turn to constantly/observe conscientiously); "religare" (to bind oneself [back]); and "reeligere" (to choose again). Because of these three different potential meanings, an etymological analysis alone does not resolve the ambiguity of defining religion, since each verb points to a different understanding of what religion is. During the Medieval Period, the term "religious" was used as a noun to describe someone who had joined a monastic order (a "religious"). The religious studies scholar Walter Capps described the purpose of the discipline as to provide "training and practice... in directing and conducting inquiry regarding the subject of religion". At the same time, Capps stated that its other purpose was to use "prescribed modes and techniques of inquiry to make the subject of religion intelligible." Religious studies scholar Robert A. Segal characterised the discipline as "a subject matter" that is "open to many approaches", and thus it "does not require either a distinctive method or a distinctive explanation to be worthy of disciplinary status." Different scholars operating in the field have different interests and intentions; some for instance seek to defend religion, while others seek to explain it away, and others wish to use religion as an example with which to prove a theory of their own. Some scholars of religious studies are interested in primarily studying the religion to which they belong. Scholars of religion have argued that a study of the subject is useful for individuals because it will provide them with knowledge that is pertinent in inter-personal and professional contexts within an increasingly globalised world. It has also been argued that studying religion is useful in appreciating and understanding sectarian tensions and religious violence.
  • 9.0K
  • 22 Nov 2022
Topic Review
Partition Problem
In number theory and computer science, the partition problem, or number partitioning, is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S1 and S2 such that the sum of the numbers in S1 equals the sum of the numbers in S2. Although the partition problem is NP-complete, there is a pseudo-polynomial time dynamic programming solution, and there are heuristics that solve the problem in many instances, either optimally or approximately. For this reason, it has been called "the easiest hard problem". There is an optimization version of the partition problem, which is to partition the multiset S into two subsets S1, S2 such that the difference between the sum of elements in S1 and the sum of elements in S2 is minimized. The optimization version is NP-hard, but can be solved efficiently in practice.
  • 8.8K
  • 10 Oct 2022
Topic Review
Lists of Mathematics Topics
This article itemizes the various lists of mathematics topics. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing. The purpose of this list is not similar to that of the Mathematics Subject Classification formulated by the American Mathematical Society. Many mathematics journals ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The subject codes so listed are used by the two major reviewing databases, Mathematical Reviews and Zentralblatt MATH. This list has some items that would not fit in such a classification, such as list of exponential topics and list of factorial and binomial topics, which may surprise the reader with the diversity of their coverage.
  • 8.8K
  • 19 Oct 2022
Topic Review
Yan Tan Tethera
Yan Tan Tethera is a sheep-counting rhyme/system traditionally used by shepherds in Northern England and earlier in some other parts of Britain. Until the Industrial Revolution, the use of traditional number systems was common among shepherds, especially in the fells of the Lake District. The Yan Tan Tethera system was also used for counting stitches in knitting. The words derive from a Brythonic Celtic language. Though most of these number systems fell out of use by 1910, some are still in use. The word yan or yen for "one" in some northern English dialects generally represents a regular development in Northern English in which the Old English long vowel /ɑː/ was broken into /ie/, /ia/ and so on. This explains the shift to yan and ane from the Old English ān, which is itself derived from the Proto-Germanic *ainaz. Another example of this development is the Northern English word for "home", hame, which has forms such as hyem, yem and yam all deriving from the Old English hām.
  • 8.8K
  • 20 Nov 2022
Topic Review
WikiLeaks
WikiLeaks (/ˈwɪkiliːks/) is an international non-profit organisation that publishes news leaks and classified media provided by anonymous sources. Its website, initiated in 2006 in Iceland by the organisation Sunshine Press, stated in 2015 that it had released online 10 million documents in its first 10 years. Julian Assange, an Australian Internet activist, is generally described as its founder and director. Since September 2018, Kristinn Hrafnsson has served as its editor-in-chief. WikiLeaks has variously described itself as an organization of journalists, political activists, mathematicians, and start-up company technologists, an intermediary between sources and journalists, an advocacy group for sources, and a public intelligence agency. The group has released a number of prominent document caches that exposed serious violations of human rights and civil liberties to the US and international public. Early releases included documentation of equipment expenditures and holdings in the Afghanistan war, a report about a corruption investigation in Kenya, and an operating procedures manual for the U.S. prison at Guantanamo Bay, Cuba. In April 2010, WikiLeaks released the Collateral Murder footage from the 12 July 2007 Baghdad airstrike in which Iraqi Reuters journalists were among several civilians killed. Other releases in 2010 included the Afghan War Diary and the "Iraq War Logs". The latter release allowed the mapping of 109,032 deaths in "significant" attacks by insurgents in Iraq that had been reported to Multi-National Force – Iraq, including about 15,000 that had not been previously published. In 2010, WikiLeaks also released classified diplomatic cables that had been sent to the US State Department. In April 2011, WikiLeaks began publishing 779 secret files relating to prisoners detained in the Guantanamo Bay detention camp. In 2012, WikiLeaks released the "Syria Files," over two million emails sent by Syrian politicians, corporations and government ministries. In 2015, WikiLeaks published Saudi Arabian diplomatic cables, documents detailing spying by the U.S. National Security Agency on successive French presidents, and the intellectual property chapter of the Trans-Pacific Partnership, a controversial international trade agreement which had been negotiated in secret. During the 2016 U.S. presidential election campaign, WikiLeaks released emails and other documents from the Democratic National Committee and from Hillary Clinton's campaign manager, John Podesta, showing that the party's national committee favoured Clinton over her rival Bernie Sanders in the primaries, leading to the resignation of DNC chairwoman Debbie Wasserman Schultz and an apology to Sanders from the DNC. These releases caused significant harm to the Clinton campaign, and have been attributed as a potential contributing factor to her loss in the general election against Donald Trump. The U.S. intelligence community expressed "high confidence" that the leaked emails had been hacked by Russia and supplied to WikiLeaks. WikiLeaks said that the source of the documents was not Russia or any other state. During the campaign, WikiLeaks promoted conspiracy theories about Hillary Clinton and the Democratic Party. In 2016, WikiLeaks released nearly 300,000 emails it described as coming from Turkey's ruling Justice and Development Party, later found to be taken from public mailing archives, and rereleased over 50,000 emails from the Turkish Minister of Energy and Natural Resources. In 2017, WikiLeaks published internal CIA documents describing tools used by the agency to hack devices including mobile phones and routers. In 2019, WikiLeaks published over 30,000 files as part of the Fishrot Files, exposing corruption at Samherji, a multinational fishing company based in Iceland. In October 2021, WikiLeaks' secure chat stopped working and in February 2022 their submission system and email server went offline. The organisation has been criticised for inadequately curating its content and violating the personal privacy of individuals. WikiLeaks has, for instance, revealed Social Security numbers, medical information, credit card numbers and details of suicide attempts.
  • 8.7K
  • 11 Oct 2022
Topic Review
Home Economics
Home economics, or family and consumer sciences, is a subject concerning human development, personal and family finances, consumer issues, housing and interior design, nutrition and food preparation, as well as textiles and apparel. Home economics courses are offered around the world and across multiple educational levels. Internationally, it is coordinated by the International Federation for Home Economics. Historically, the purpose of these courses was to professionalize housework, to provide intellectual fulfillment for women, and to emphasize the value of "women's work" in society and to prepare them for the traditional roles of sexes. However, it has since evolved into family and consumer sciences to cover additional subject matter outside of just home life and wellness. Family and consumer sciences are taught as an elective or required course in secondary education, as a continuing education course in institutions, and at the primary level.   Beginning as home economics in the United States, the course was a key part of the education system for teaching one the art of taking care of a household. In the 19th and early 20th century, it was a woman-dominated course, teaching women to be homemakers and efficient household managers. The American Association of Family and Consumer Sciences was created as an answer to more Americans desiring youth to learn vocational skills. Politics played a role in home economics education, and it wasn’t until later in the century that the course shifted from being woman-dominated to now required for both sexes.   Now family and consumer science have been included in the broader subject of Career Technical Education, a program that teaches skilled trades, applied sciences, modern technologies, and career preparation. Despite the subjects over the past century, there has been a major decline in home economics courses offered by educational institutions.  
  • 8.7K
  • 09 Nov 2022
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