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Mathematics ( 4921 views )

Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes the study of such topics as quantity, structure, space, and change.Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics, or mathematics for its own sake, without having any application in mind. Practical applications for what began as pure mathematics are often discovered.

Mathematics and art ( 4844 views )

Mathematics and art
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.
Mathematics and art have a long historical relationship. Artists have used mathematics since the 4th century BC when the Greek sculptor Polykleitos wrote his Canon, prescribing proportions based on the ratio 1:√2 for the ideal male nude. Persistent popular claims have been made for the use of the golden ratio in ancient art and architecture, without reliable evidence. In the Italian Renaissance, Luca Pacioli wrote the influential treatise De Divina Proportione (1509), illustrated with woodcuts by Leonardo da Vinci, on the use of the golden ratio in art. Another Italian painter, Piero della Francesca, developed Euclid's ideas on perspective in treatises such as De Prospectiva Pingendi, and in his paintings. The engraver Albrecht Dürer made many references to mathematics in his work Melencolia I. In modern times, the graphic artist M. C. Escher made intensive use of tessellation and hyperbolic geometry, with the help of the mathematician H. S. M. Coxeter, while the De Stijl movement led by Theo van Doesburg and Piet Mondrian explicitly embraced geometrical forms. Mathematics has inspired textile arts such as quilting, knitting, cross-stitch, crochet, embroidery, weaving, Turkish and other carpet-making, as well as kilim. In Islamic art, symmetries are evident in forms as varied as Persian girih and Moroccan zellige tilework, Mughal jali pierced stone screens, and widespread muqarnas vaulting.
Mathematics has directly influenced art with conceptual tools such as linear perspective, the analysis of symmetry, and mathematical objects such as polyhedra and the Möbius strip. Magnus Wenninger creates colourful stellated polyhedra, originally as models for teaching. Mathematical concepts such as recursion and logical paradox can be seen in paintings by Rene Magritte and in engravings by M. C. Escher. Computer art often makes use of fractals including the Mandelbrot set, and sometimes explores other mathematical objects such as cellular automata. Controversially, the artist David Hockney has argued that artists from the Renaissance onwards made use of the camera lucida to draw precise representations of scenes; the architect Philip Steadman similarly argued that Vermeer used the camera obscura in his distinctively observed paintings.
Other relationships include the algorithmic analysis of artworks by X-ray fluorescence spectroscopy, the finding that traditional batiks from different regions of Java have distinct fractal dimensions, and stimuli to mathematics research, especially Filippo Brunelleschi's theory of perspective, which eventually led to Girard Desargues's projective geometry. A persistent view, based ultimately on the Pythagorean notion of harmony in music, holds that everything was arranged by Number, that God is the geometer of the world, and that therefore the world's geometry is sacred, as seen in artworks such as William Blake's The Ancient of Days.

Matheson Tri-Gas ( 144 views )

Matheson Tri-Gas
Matheson Tri-Gas, Inc. is a supplier of industrial gases, medical gases, specialty and electronic gases, propane, gas handling equipment, gas purification systems, industrial safety equipment, and gas engineering services. It is headquartered in Irving, Texas, with more than 300 retail, plant and warehouse locations in the United States. Matheson supplies its gas products through all distribution methods: cylinder, bulk and pipeline.
Matheson is the North American operating entity, and the largest subsidiary of Taiyo Nippon Sanso Corporation (TYO: 4091), one of the top five suppliers of industrial, specialty, and electronics gases in the world, and the largest in Japan. Matheson Tri-Gas, Inc. adds to TNSC's reach with its own operations in China, Belgium, Korea, and India. TNSC is a consolidated subsidiary of Mitsubishi Chemical Holdings.

Matrix (mathematics) ( 6559 views )

Matrix (mathematics)
Licensed under Creative Commons Attribution-Share Alike 4.0 (Lakeworks).

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimensions of the matrix below are 2 × 3 (read "two by three"), because there are two rows and three columns:
[
1
9
−
13
20
5
−
6
]
.
{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.}
Provided that they have the same size (each matrix has the same number of rows and the same number of columns as the other), two matrices can be added or subtracted element by element (see Conformable matrix). The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second (i.e., the inner dimensions are the same, n for an (m×n)-matrix times an (n×p)-matrix, resulting in an (m×p)-matrix. There is no product the other way round, a first hint that matrix multiplication is not commutative. Any matrix can be multiplied element-wise by a scalar from its associated field.
The individual items in an m×n matrix A, often denoted by ai,j, where i and j usually vary from 1 to m and n, respectively, are called its elements or entries. For conveniently expressing an element of the results of matrix operations the indices of the element are often attached to the parenthesized or bracketed matrix expression; e.g.: (AB)i,j refers to an element of a matrix product. In the context of abstract index notation this ambiguously refers also to the whole matrix product.
A major application of matrices is to represent linear transformations, that is, generalizations of linear functions such as f(x) = 4x. For example, the rotation of vectors in three-dimensional space is a linear transformation, which can be represented by a rotation matrix R: if v is a column vector (a matrix with only one column) describing the position of a point in space, the product Rv is a column vector describing the position of that point after a rotation. The product of two transformation matrices is a matrix that represents the composition of two transformations. Another application of matrices is in the solution of systems of linear equations. If the matrix is square, it is possible to deduce some of its properties by computing its determinant. For example, a square matrix has an inverse if and only if its determinant is not zero. Insight into the geometry of a linear transformation is obtainable (along with other information) from the matrix's eigenvalues and eigenvectors.
Applications of matrices are found in most scientific fields. In every branch of physics, including classical mechanics, optics, electromagnetism, quantum mechanics, and quantum electrodynamics, they are used to study physical phenomena, such as the motion of rigid bodies. In computer graphics, they are used to manipulate 3D models and project them onto a 2-dimensional screen. In probability theory and statistics, stochastic matrices are used to describe sets of probabilities; for instance, they are used within the PageRank algorithm that ranks the pages in a Google search. Matrix calculus generalizes classical analytical notions such as derivatives and exponentials to higher dimensions. Matrices are used in economics to describe systems of economic relationships.
A major branch of numerical analysis is devoted to the development of efficient algorithms for matrix computations, a subject that is centuries old and is today an expanding area of research. Matrix decomposition methods simplify computations, both theoretically and practically. Algorithms that are tailored to particular matrix structures, such as sparse matrices and near-diagonal matrices, expedite computations in finite element method and other computations. Infinite matrices occur in planetary theory and in atomic theory. A simple example of an infinite matrix is the matrix representing the derivative operator, which acts on the Taylor series of a function.

Matryoshka doll ( 7011 views )

Matryoshka doll
Licensed under Creative Commons Attribution-Share Alike 3.0 (No machine-readable author provided. Fanghong assumed (based on copyright claims).).

A matryoshka doll (Russian: матрёшка, IPA: [mɐˈtrʲɵʂkə] ( listen)), also known as a Russian nesting doll, stacking dolls, or Russian doll, is a set of wooden dolls of decreasing size placed one inside another. The name "matryoshka" (матрёшка), literally "little matron", is a diminutive form of Russian female first name "Matryona" (Матрёна) or "Matriosha".A set of matryoshkas consists of a wooden figure which separates, top from bottom, to reveal a smaller figure of the same sort inside, which has, in turn, another figure inside of it, and so on.
The first Russian nested doll set was made in 1890 by Vasily Zvyozdochkin from a design by Sergey Malyutin, who was a folk crafts painter at Abramtsevo. Traditionally the outer layer is a woman, dressed in a sarafan, a long and shapeless traditional Russian peasant jumper dress. The figures inside may be of either gender; the smallest, innermost doll is typically a baby turned from a single piece of wood. Much of the artistry is in the painting of each doll, which can be very elaborate. The dolls often follow a theme; the themes may vary, from fairy tale characters to Soviet leaders. In the west, Matryoshka dolls are often mistakenly referred to as "babushka dolls", babushka meaning "grandmother" or "old woman".

Matterhorn ( 8961 views )

Matterhorn
Licensed under Creative Commons Attribution-Share Alike 3.0 (

- Photo: chil, on Camptocamp.org
- Derivative work:Zacharie Grossen

The Matterhorn (German: Matterhorn, [ˈmatərˌhɔrn]; Italian: Cervino, [ˈtʃerˈviːno]; French: Le Cervin, [mɔ̃ sɛʁvɛ̃]) is a mountain of the Alps, straddling the main watershed and border between Switzerland and Italy. It is a huge and near-symmetrical pyramidal peak in the extended Monte Rosa area of the Pennine Alps, whose summit is 4,478 metres (14,692 ft) high, making it one of the highest summits in the Alps and Europe. The four steep faces, rising above the surrounding glaciers, face the four compass points and are split by the Hörnli, Furggen, Leone, and Zmutt ridges. The mountain overlooks the Swiss town of Zermatt, in the canton of Valais, to the north-east and the Italian town of Breuil-Cervinia in the Aosta Valley to the south. Just east of the Matterhorn is Theodul Pass, the main passage between the two valleys on its north and south sides, and a trade route since the Roman Era.
The Matterhorn was studied by Horace-Bénédict de Saussure in the late eighteenth century, who was followed by other renowned naturalists and artists, such as John Ruskin, in the nineteenth century. It remained unclimbed after most of the other great Alpine peaks had been attained and became the subject of an international competition for the summit. The first ascent of the Matterhorn was finally made in 1865 from Zermatt, by a party led by Edward Whymper, but ended disastrously when four of its members fell to their deaths on the descent. That climb and disaster, later portrayed in several films, marked the end of the golden age of alpinism. The north face was not climbed until 1931 and is amongst the three biggest north faces of the Alps, known as "The Trilogy". The west face, which is the highest of the Matterhorn's four faces, was completely climbed only in 1962. It is estimated that over 500 alpinists have died on the Matterhorn since the first climb in 1865, making it one of the deadliest peaks in the world.
The Matterhorn is mainly composed of gneisses (originally fragments of the African Plate before the Alpine orogeny) from the Dent Blanche nappe, lying over ophiolites and sedimentary rocks of the Penninic nappes. The mountain's current shape is the result of cirque erosion due to multiple glaciers diverging from the peak, such as the Matterhorn Glacier at the base of the north face, forming a horn.
Sometimes referred to as the Mountain of Mountains (German: Berg der Berge), the Matterhorn has become an iconic emblem of the Swiss Alps and of the Alps in general. Since the end of the 19th century, when railways were built in the area, the mountain has attracted increasing numbers of visitors and climbers. Each year, numerous mountaineers try to climb the Matterhorn from the Hörnli Hut via the northeast Hörnli ridge, the most popular route to the summit. Many trekkers also undertake the 10-day-long circuit around the mountain. The Matterhorn has been part of the Swiss Federal Inventory of Natural Monuments since 1983.

Maxim Integrated ( 62 views )

Maxim Integrated
Maxim Integrated is an American, publicly traded company that designs, manufactures, and sells analog and mixed-signal integrated circuits.Maxim Integrated develops integrated circuits (ICs) for the automotive, industrial, communications, consumer, and computing markets. The company is headquartered in San Jose, California, and has design centers, manufacturing facilities, and sales offices throughout the world. In the fiscal year 2019, it had US$2.31 billion in sales, 7,131 employees, and 35,000 customers worldwide. Maxim is a Fortune 1000 company and its stock is a component of the NASDAQ-100 stock market index. In December 2018, Maxim was added back to the S&P 500.

May Day ( 3952 views )

May Day
Licensed under Creative Commons Attribution-Share Alike 2.0 (Kevin Gordon).

May Day is a public holiday usually celebrated on 1 May. It is an ancient Northern Hemisphere spring festival and a traditional spring holiday in many cultures. Dances, singing, and cake are usually part of the festivities. In the late 19th century, May Day was chosen as the date for International Workers' Day by the Socialists and Communists of the Second International to commemorate the Haymarket affair in Chicago. International Workers' Day can also be referred to as "May Day", but it is a different celebration from the traditional May Day.

Maya architecture ( 3447 views )

Maya architecture
A unique and intricate style, the tradition of Maya architecture spans several thousands of years. Often, the buildings most dramatic and easily recognizable as Mayans are the stepped pyramids of the Terminal Pre-classic period and beyond. Being based on the general Mesoamerican architectural traditions, these pyramids relied on intricate carved stone in order to create a stairstep design. Each pyramid was dedicated to a deity whose shrine sat at its peak. During this "height" of Maya culture, the centers of their religious, commercial and bureaucratic power grew into large cities, namely Tikal and Uxmal. Through observation of the numerous consistent elements and stylistic distinctions, remnants of Maya architecture have become an important key to understanding the evolution of their ancient temples.