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Illumination Problem
Illumination problems are a class of mathematical problems that study the illumination of rooms with mirrored walls by point light sources. Original formulation The original formulation was attributed to Ernst Straus in the 1950s and has been resolved. Straus asked whether a room with mirrored walls can always be illuminated by a single point light source, allowing for repeated reflection of light off the mirrored walls. Alternatively, the question can be stated as asking that if a billiard table can be constructed in any required shape, is there a shape possible such that there is a point where it is impossible to hit the billiard ball at another point, assuming the ball is point-like and continues infinitely rather than stopping due to friction. Penrose unilluminable room The original problem was first solved in 1958 by Roger Penrose using ellipses to form the Penrose unilluminable room. He showed that there exists a room with curved walls that must always have dark regions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penrose Unilluminable Room
Illumination problems are a class of mathematical problems that study the illumination (lighting), illumination of rooms with mirrored walls by point light sources. Original formulation The original formulation was attributed to Ernst Straus in the 1950s and has been resolved. Straus asked whether a room with mirrored walls can always be illuminated by a single point light source, allowing for repeated reflection of light off the mirrored walls. Alternatively, the question can be stated as asking that if a billiard table can be constructed in any required shape, is there a shape possible such that there is a point where it is impossible to hit the cue ball, billiard ball at another point, assuming the ball is point-like and continues infinitely rather than stopping due to friction. Penrose unilluminable room The original problem was first solved in 1958 by Roger Penrose using ellipses to form the Penrose unilluminable room. He showed that there exists a room with curved walls that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Magazine
''Quantum: The Magazine of Math and Science'' was a United States-based bimonthly magazine of mathematics and science, primarily physics, designed for young readers. It was published by the National Science Teachers Association (NSTA) and Springer-Verlag and was headquartered in Washington DC ) , image_skyline = , image_caption = Clockwise from top left: the Washington Monument and Lincoln Memorial on the National Mall, United States Capitol, Logan Circle, Jefferson Memorial, White House, Adams Morgan, .... ''Quantum'' was a sister publication of the Russian magazine '' Kvant''. ''Quantum'' contained translations from ''Kvant'' and original material. The magazine was founded in 1990. It ceased publication with its July/August 2001 issue. Two books derived from ''Quantum'' materials have been published: ''Quantoons'' and ''Quantum Quandaries''. All articles from the magazine are indexed online by the NSTA. References External links WorldCat i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfram Demonstrations Project
The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields. It is hosted by Wolfram Research, whose stated goal is to bring computational exploration to a large population. At its launch, it contained 1300 demonstrations but has grown to over 10,000. The site won a Parents' Choice Award in 2008. Technology The Demonstrations run in '' Mathematica'' 6 or above and in '' Wolfram CDF Player'' which is a free modified version of Wolfram's ''Mathematica'' and available for Windows, Linux and macOS and can operate as a web browser plugin. They typically consist of a very direct user interface to a graphic or visualization, which dynamically recomputes in response to user actions such as moving a slider, clicking a button, or dragging a piece of graphics. Each Demonstration also has a brief description of the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steve Mould
Steve Mould (born 5 October 1978) is a British educational YouTuber, author, and science presenter who is most notable for making science-related educational videos on his YouTube channel. Early life Mould was born on 5 October 1978 in Gateshead, United Kingdom. He went to St Thomas More Catholic School, Blaydon, before going on to study physics at St Hugh's College, Oxford. Career In 2014, Mould co-hosted ITV's ''I Never Knew That About Britain'' alongside Paul Martin and Suzannah Lipscomb. He has also appeared as a science expert on ''The Alan Titchmarsh Show'', ''The One Show'', and ''Blue Peter''. Mould's YouTube video on rising self-siphoning beads, in which he demonstrated the phenomenon and proposed an explanation, brought the problem to the attention of academics John Biggins and Mark Warner of Cambridge University, who published their findings about what has now been called the "chain fountain" in ''Proceedings of the Royal Society A''. Warner has referred to it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numberphile
''Numberphile'' is an educational YouTube channel featuring videos that explore topics from a variety of fields of mathematics. In the early days of the channel, each video focused on a specific number, but the channel has since expanded its scope, featuring videos on more advanced mathematical concepts such as Fermat's Last Theorem, the Riemann hypothesis and Kruskal's tree theorem. The videos are produced by Brady Haran, a former BBC video journalist and creator of Periodic Videos, Sixty Symbols, and several other YouTube channels. Videos on the channel feature several university professors, maths communicators and famous mathematicians. In 2018, Haran released a spin-off audio podcast titled ''The Numberphile Podcast''. YouTube channel The ''Numberphile'' YouTube channel was started on 15 September 2011. Most videos consist of Haran interviewing an expert on a number, mathematical theorem or other mathematical concept. The expert usually draws out their explanation on a la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
YouTube
YouTube is a global online video platform, online video sharing and social media, social media platform headquartered in San Bruno, California. It was launched on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim. It is owned by Google, and is the List of most visited websites, second most visited website, after Google Search. YouTube has more than 2.5 billion monthly users who collectively watch more than one billion hours of videos each day. , videos were being uploaded at a rate of more than 500 hours of content per minute. In October 2006, YouTube was bought by Google for $1.65 billion. Google's ownership of YouTube expanded the site's business model, expanding from generating revenue from advertisements alone, to offering paid content such as movies and exclusive content produced by YouTube. It also offers YouTube Premium, a paid subscription option for watching content without ads. YouTube also approved creators to participate in Google's Google AdSens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry & Topology
''Geometry & Topology'' is a peer-refereed, international mathematics research journal devoted to geometry and topology, and their applications. It is currently based at the University of Warwick, United Kingdom, and published by Mathematical Sciences Publishers, a nonprofit academic publishing organisation. It was founded in 1997Allyn Jackson The slow revolution of the free electronic journal Notices of the American Mathematical Society, vol. 47 (2000), no. 9, pp. 1053-1059 by a group of topologists who were dissatisfied with recent substantial rises in subscription prices of journals published by major publishing corporations. The aim was to set up a high-quality journal, capable of competing with existing journals, but with substantially lower subscription fees. The journal was open-access for its first ten years of existence and was available free to individual users, although institutions were required to pay modest subscription fees for both online access and for printed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Review
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics. SIAM is one of the four member organizations of the Joint Policy Board for Mathematics. Membership Membership is open to both individuals and organizations. By the end of its first full year of operation, SIAM had 130 memb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it is the oldest continuously published magazine in the United States. ''Scientific American'' is owned by Springer Nature, which in turn is a subsidiary of Holtzbrinck Publishing Group. History ''Scientific American'' was founded by inventor and publisher Rufus Porter (painter), Rufus Porter in 1845 as a four-page weekly newspaper. The first issue of the large format newspaper was released August 28, 1845. Throughout its early years, much emphasis was placed on reports of what was going on at the United States Patent and Trademark Office, U.S. Patent Office. It also reported on a broad range of inventions including perpetual motion machines, an 1860 device for buoying vessels by Abraham Lincoln, and the universal joint which now can be found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygonal
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two together, may be called a polygon. The segments of a polygonal circuit are called its '' edges'' or ''sides''. The points where two edges meet are the polygon's '' vertices'' (singular: vertex) or ''corners''. The interior of a solid polygon is sometimes called its ''body''. An ''n''-gon is a polygon with ''n'' sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of simple polygons and they often define a polygon accordingly. A polygonal boundary may be allowed to cross over itself, creating star polygons and other self-intersecting polygons. A polygon is a 2-dimensional example of the more general polytope in any numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Problem
A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems. It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. Real-world problems Informal "real-world" mathematical problems are questions related to a concrete setting, such as "Adam has five apples and gives John three. How many has he left?". Such questions are usually more difficult to solve than regular mathematical exercises like "5 − 3", even if one knows the mathematics required to solve the problem. Known as word problems, they are used in mathematics education to teach students to connect real-world situations to the abstract language of mathematics. In general, to use mathematics for solving a real-world problem, the first ste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
