text stringlengths 14 4.79k | source stringlengths 13 304 | tokens float64 75 1.06k ⌀ | char_length float64 106 4.79k ⌀ | article_title stringlengths 16 300 ⌀ |
|---|---|---|---|---|
Mathematician Kurt Gödel provided a formal argument for God's existence. The argument was constructed by Gödel but not published until long after his death. He provided an argument based on modal logic; he uses the conception of properties, ultimately concluding with God's existence. | Wikipedia - Ontological Proof | null | null | null |
Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B Definition 3: x necessarily exists if and only if every essence of x is neces... | Wikipedia - Ontological Proof | null | null | null |
He warned against interpreting "positive" as being morally or aesthetically "good" (the greatest advantage and least disadvantage), as this includes negative characteristics. Instead, he suggested that "positive" should be interpreted as being perfect, or "purely good", without negative characteristics.Gödel's listed t... | Wikipedia - Ontological Proof | null | null | null |
Or, for Axiom 1, to use another example, the negation of a positive property both includes the lack of any properties and the opposite property, and only the lack of any properties is a privation of a property, not the opposite property (for instance, the lack of happiness can symbolize either sadness or having no emot... | Wikipedia - Ontological Proof | null | null | null |
Mathematician Richard Schwartz has studied outer billiards on kites. Outer billiards is a dynamical system in which, from a point outside a given compact convex set in the plane, one draws a tangent line to the convex set, travels from the starting point along this line to another point equally far from the point of ta... | Wikipedia - Kite (geometry) | null | null | null |
For this problem, any affine transformation of a kite preserves the dynamical properties of outer billiards on it, and it is possible to transform any kite into a shape where three vertices are at the points ( − 1 , 0 ) {\displaystyle (-1,0)} and ( 0 , ± 1 ) {\displaystyle (0,\pm 1)} , with the fourth at ( α , 0 ) {\di... | Wikipedia - Kite (geometry) | null | null | null |
Mathematician William Lawvere interpreted dialectics in the setting of categorical logic in terms of adjunctions between idempotent monads. This perspective may be useful in the context of theoretical computer science where the duality between syntax and semantics can be interpreted as a dialectic in this sense. For ex... | Wikipedia - Hegel's dialectic | null | null | null |
Mathematician Zhu Shijie further developed rod calculus to include polynomial equations of 2 to four unknowns. For example, polynomials of three unknowns: Equation 1: − y − z − y 2 ∗ x − x + x y z = 0 {\displaystyle -y-z-y^{2}*x-x+xyz=0} 太 Equation 2: − y − z + x − x 2 + x z = 0 {\displaystyle -y-z+x-x^{2}+xz=0} Equati... | Wikipedia - Rod calculus | null | null | null |
Mathematicians (and those in related sciences) very frequently speak of whether a mathematical object—a function, a set, a space of one sort or another—is "well-behaved". While the term has no fixed formal definition, it generally refers to the quality of satisfying a list of prevailing conditions, which might be depen... | Wikipedia - Pathological (mathematics) | null | null | null |
This has the benefit of making analysis easier, but produces a loss of generality of any conclusions reached. In both pure and applied mathematics (e.g., optimization, numerical integration, mathematical physics), well-behaved also means not violating any assumptions needed to successfully apply whatever analysis is be... | Wikipedia - Pathological (mathematics) | null | null | null |
It is not unusual to have situations in which most cases (in terms of cardinality or measure) are pathological, but the pathological cases will not arise in practice—unless constructed deliberately. The term "well-behaved" is generally applied in an absolute sense—either something is well-behaved or it is not. For exam... | Wikipedia - Pathological (mathematics) | null | null | null |
In Bézout's theorem, two polynomials are well-behaved, and thus the formula given by the theorem for the number of their intersections is valid, if their polynomial greatest common divisor is a constant. A meromorphic function is a ratio of two well-behaved functions, in the sense of those two functions being holomorph... | Wikipedia - Pathological (mathematics) | null | null | null |
In probability, events contained in the probability space's corresponding sigma-algebra are well-behaved, as are measurable functions.Unusually, the term could also be applied in a comparative sense: In calculus: Analytic functions are better-behaved than general smooth functions. Smooth functions are better-behaved th... | Wikipedia - Pathological (mathematics) | null | null | null |
The larger the number of times the function can be differentiated, the more well-behaved it is. Continuous functions are better-behaved than Riemann-integrable functions on compact sets. Riemann-integrable functions are better-behaved than Lebesgue-integrable functions. | Wikipedia - Pathological (mathematics) | null | null | null |
Lebesgue-integrable functions are better-behaved than general functions. In topology, continuous functions are better-behaved than discontinuous ones. Euclidean space is better-behaved than non-Euclidean geometry. | Wikipedia - Pathological (mathematics) | null | null | null |
Attractive fixed points are better-behaved than repulsive fixed points. Hausdorff topologies are better-behaved than those in arbitrary general topology. Borel sets are better-behaved than arbitrary sets of real numbers. | Wikipedia - Pathological (mathematics) | null | null | null |
Spaces with integer dimension are better-behaved than spaces with fractal dimension. In abstract algebra: Groups are better-behaved than magmas and semigroups. Abelian groups are better-behaved than non-Abelian groups. | Wikipedia - Pathological (mathematics) | null | null | null |
Finitely-generated Abelian groups are better-behaved than non-finitely-generated Abelian groups. Finite-dimensional vector spaces are better-behaved than infinite-dimensional ones. | Wikipedia - Pathological (mathematics) | null | null | null |
Fields are better-behaved than skew fields or general rings. Separable field extensions are better-behaved than non-separable ones. Normed division algebras are better-behaved than general composition algebras. | Wikipedia - Pathological (mathematics) | null | null | null |
Mathematicians have a professional responsibility to support the ethical use of mathematics in practice, both to sustain the reputation of the profession and to protect society from the impacts of unethical behavior. For example, mathematics is extensively applied in the use of Big Data in Artificial Intelligence appli... | Wikipedia - Ethics in mathematics | null | null | null |
Mathematicians have always had differing opinions regarding the distinction between pure and applied mathematics. One of the most famous (but perhaps misunderstood) modern examples of this debate can be found in G.H. Hardy's 1940 essay A Mathematician's Apology. It is widely believed that Hardy considered applied mathe... | Wikipedia - Pure Mathematics | null | null | null |
Although it is true that Hardy preferred pure mathematics, which he often compared to painting and poetry, Hardy saw the distinction between pure and applied mathematics to be simply that applied mathematics sought to express physical truth in a mathematical framework, whereas pure mathematics expressed truths that wer... | Wikipedia - Pure Mathematics | null | null | null |
Moreover, Hardy briefly admitted that—just as the application of matrix theory and group theory to physics had come unexpectedly—the time may come where some kinds of beautiful, "real" mathematics may be useful as well. Another insightful view is offered by American mathematician Andy Magid: I've always thought that a ... | Wikipedia - Pure Mathematics | null | null | null |
An uninformed observer might think that these represent a dichotomy, but in fact the latter subsumes the former: a non-commutative ring is a not-necessarily-commutative ring. If we use similar conventions, then we could refer to applied mathematics and nonapplied mathematics, where by the latter we mean not-necessarily... | Wikipedia - Pure Mathematics | null | null | null |
: 36 He further argued that "Before one came upon the idea of deducing the form of a cylinder from the rotation of a rectangle about one of its sides, a number of real rectangles and cylinders, however imperfect in form, must have been examined. Like all other sciences, mathematics arose out of the needs of men...But, ... | Wikipedia - Pure Mathematics | null | null | null |
Mathematicians in industrial, scientific, military and intelligence roles crucially influence decisions with significant consequences. | Wikipedia - Ethics in mathematics | null | null | null |
Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With profe... | Wikipedia - Applied mathematician | null | null | null |
Mathematicians study and research in all the different areas of mathematics. The publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals, many of them devoted to mathematics and many devoted to subjects to which mathematics is applied (such as theoretical computer s... | Wikipedia - Lists of mathematics topics | null | null | null |
Mathematicians use some technical terms when discussing tilings. An edge is the intersection between two bordering tiles; it is often a straight line. A vertex is the point of intersection of three or more bordering tiles. Using these terms, an isogonal or vertex-transitive tiling is a tiling where every vertex point i... | Wikipedia - Euclidean tiling | null | null | null |
The fundamental region is a shape such as a rectangle that is repeated to form the tessellation. For example, a regular tessellation of the plane with squares has a meeting of four squares at every vertex.The sides of the polygons are not necessarily identical to the edges of the tiles. An edge-to-edge tiling is any po... | Wikipedia - Euclidean tiling | null | null | null |
In an edge-to-edge tiling, the sides of the polygons and the edges of the tiles are the same. The familiar "brick wall" tiling is not edge-to-edge because the long side of each rectangular brick is shared with two bordering bricks.A normal tiling is a tessellation for which every tile is topologically equivalent to a d... | Wikipedia - Euclidean tiling | null | null | null |
A monohedral tiling is a tessellation in which all tiles are congruent; it has only one prototile. A particularly interesting type of monohedral tessellation is the spiral monohedral tiling. The first spiral monohedral tiling was discovered by Heinz Voderberg in 1936; the Voderberg tiling has a unit tile that is a nonc... | Wikipedia - Euclidean tiling | null | null | null |
The Hirschhorn tiling, published by Michael D. Hirschhorn and D. C. Hunt in 1985, is a pentagon tiling using irregular pentagons: regular pentagons cannot tile the Euclidean plane as the internal angle of a regular pentagon, 3π/5, is not a divisor of 2π.An isohedral tiling is a special variation of a monohedral tiling ... | Wikipedia - Euclidean tiling | null | null | null |
There are only three regular tessellations: those made up of equilateral triangles, squares, or regular hexagons. All three of these tilings are isogonal and monohedral. A semi-regular (or Archimedean) tessellation uses more than one type of regular polygon in an isogonal arrangement. | Wikipedia - Euclidean tiling | null | null | null |
There are eight semi-regular tilings (or nine if the mirror-image pair of tilings counts as two). These can be described by their vertex configuration; for example, a semi-regular tiling using squares and regular octagons has the vertex configuration 4.82 (each vertex has one square and two octagons). Many non-edge-to-... | Wikipedia - Euclidean tiling | null | null | null |
Mathematics & Mechanics of Solids is abstracted and indexed in, among other databases: SCOPUS, and the Social Sciences Citation Index. According to the Journal Citation Reports, its 2016 impact factor is 2.953, ranking it 72 out of 275 journals in the category ‘Materials Science, Multidisciplinary’. and 11 out of 100 j... | Wikipedia - Mathematics & Mechanics of Solids | null | null | null |
Mathematics (Calculus, differential equations, statistics) Physics Chemistry Engineering Mechanics (Statics, Dynamics, Solids Mechanics) Fluid Mechanics Thermodynamics | Wikipedia - Natural resources engineering | null | null | null |
Mathematics Today is a general-interest mathematics publication aimed primarily at Institute members, published six times a year and containing articles, reviews, reports and other news on developments in mathematics and its applications. | Wikipedia - Transactions of Mathematics and its Applications | null | null | null |
Mathematics and Mechanics of Solids is an international journal which publishes original research in solid mechanics and materials science. The journal’s aim is to publish original, self-contained research that focuses on the mechanical behaviour of solids with particular emphasis on mathematical principles. | Wikipedia - Mathematics & Mechanics of Solids | null | null | null |
Mathematics and art are related in a variety of ways. For instance, the theory of perspective showed that there is more to geometry than just the metric properties of figures: perspective is the origin of projective geometry.Artists have long used concepts of proportion in design. Vitruvius developed a complicated theo... | Wikipedia - Geometric object | null | null | null |
Often claimed to be the most aesthetically pleasing ratio of lengths, it is frequently stated to be incorporated into famous works of art, though the most reliable and unambiguous examples were made deliberately by artists aware of this legend.Tilings, or tessellations, have been used in art throughout history. Islamic... | Wikipedia - Geometric object | null | null | null |
Mathematics and physics have influenced each other over their modern history. Modern physics uses mathematics abundantly, and is also the motivation of major mathematical developments. | Wikipedia - Fields of mathematics | null | null | null |
Mathematics can be discerned in many of the arts, such as music, dance, painting, architecture, and sculpture. Each of these is richly associated with mathematics. Among the connections to the visual arts, mathematics can provide tools for artists, such as the rules of linear perspective as described by Brook Taylor an... | Wikipedia - Mathematics and art | null | null | null |
The use of perspective began, despite some embryonic usages in the architecture of Ancient Greece, with Italian painters such as Giotto in the 13th century; rules such as the vanishing point were first formulated by Brunelleschi in about 1413, his theory influencing Leonardo and Dürer. Isaac Newton's work on the optica... | Wikipedia - Mathematics and art | null | null | null |
Tools may be applied by mathematicians who are exploring art, or artists inspired by mathematics, such as M. C. Escher (inspired by H. S. M. Coxeter) and the architect Frank Gehry, who more tenuously argued that computer aided design enabled him to express himself in a wholly new way. The artist Richard Wright argues t... | Wikipedia - Mathematics and art | null | null | null |
Wright concludes by stating that it is appropriate to subject mathematical objects to any methods used to "come to terms with cultural artifacts like art, the tension between objectivity and subjectivity, their metaphorical meanings and the character of representational systems." He gives as instances an image from the... | Wikipedia - Mathematics and art | null | null | null |
Sasho Kalajdzievski's Math and Art: An Introduction to Visual Mathematics takes a similar approach, looking at suitably visual mathematics topics such as tilings, fractals and hyperbolic geometry.Some of the first works of computer art were created by Desmond Paul Henry's "Drawing Machine 1", an analogue machine based ... | Wikipedia - Mathematics and art | null | null | null |
Mathematics education Numeracy Numerical Cognition Subitizing Mathematical anxiety Dyscalculia Acalculia Ageometresia Number sense Numerosity adaptation effect Approximate number system Mathematical maturity | Wikipedia - Outline of mathematics | null | null | null |
Mathematics education reform built up momentum in the early 1980s, as educators reacted to the "new math" of the 1960s and 1970s. The work of Piaget and other developmental psychologists had shifted the focus of mathematics educators from mathematics content to how children best learn mathematics. The National Council ... | Wikipedia - Homeschool mathematics | null | null | null |
In contrast, "traditional" textbooks emphasize procedural mathematics and provide step-by-step examples with skill-building exercises. Traditional mathematics focuses on teaching algorithms that will lead to the correct answer of a particular problem. Because of this focus on application of algorithms, the student of t... | Wikipedia - Homeschool mathematics | null | null | null |
Reform mathematics de-emphasizes this algorithmic dependence. Instead of leading students to find the exact answers to specific problems, reform educators focus students on the overall process which leads to an answer. | Wikipedia - Homeschool mathematics | null | null | null |
Students' occasional errors are deemed less important than their understanding of an overall thought process. Research has shown that children make fewer mistakes with calculations and remember algorithms longer when they understand the concepts underlying the methods they use. In general, children in reform classes pe... | Wikipedia - Homeschool mathematics | null | null | null |
Mathematics has a remarkable ability to cross cultural boundaries and time periods. As a human activity, the practice of mathematics has a social side, which includes education, careers, recognition, popularization, and so on. In education, mathematics is a core part of the curriculum and forms an important element of ... | Wikipedia - Fields of mathematics | null | null | null |
Comparable evidence has been unearthed for scribal mathematics training in the ancient Near East and then for the Greco-Roman world starting around 300 BCE. The oldest known mathematics textbook is the Rhind papyrus, dated from c. | Wikipedia - Fields of mathematics | null | null | null |
1650 BCE in Egypt. Due to a scarcity of books, mathematical teachings in ancient India were communicated using memorized oral tradition since the Vedic period (c. 1500 – c. | Wikipedia - Fields of mathematics | null | null | null |
500 BCE). In Imperial China during the Tang dynasty (618–907 CE), a mathematics curriculum was adopted for the civil service exam to join the state bureaucracy.Following the Dark Ages, mathematics education in Europe was provided by religious schools as part of the Quadrivium. Formal instruction in pedagogy began with ... | Wikipedia - Fields of mathematics | null | null | null |
Most mathematical curriculum remained at a basic and practical level until the nineteenth century, when it began to flourish in France and Germany. The oldest journal addressing instruction in mathematics was L'Enseignement Mathématique, which began publication in 1899. The Western advancements in science and technolog... | Wikipedia - Fields of mathematics | null | null | null |
While the content of courses varies, in the present day nearly all countries teach mathematics to students for significant amounts of time.During school, mathematical capabilities and positive expectations have a strong association with career interest in the field. Extrinsic factors such as feedback motivation by teac... | Wikipedia - Fields of mathematics | null | null | null |
This is known as math anxiety or math phobia, and is considered the most prominent of the disorders impacting academic performance. Math anxiety can develop due to various factors such as parental and teacher attitudes, social stereotypes, and personal traits. Help to counteract the anxiety can come from changes in ins... | Wikipedia - Fields of mathematics | null | null | null |
Mathematics has been used to understand juggling as juggling has been used to test mathematics. The number of possible patterns n digits long using b or fewer balls is bn and the average of the numbers in a siteswap pattern equal the number of balls required for the pattern. For example, the number of three digit three... | Wikipedia - Mathematics of juggling | null | null | null |
For example, "the fountain pattern...can be stably performed in two ways...one can perform the fountain with different frequencies for the two hands, but that coordination is difficult because of the tendency of the limbs to synchronize," while "in the cascade...the crossing of the balls between the hands demands that ... | Wikipedia - Mathematics of juggling | null | null | null |
Mathematics in Glaciology consists of theoretical, experimental, and modeling. It usually covers glaciers, sea ice, waterflow, and the land under the glacier. Polycrystalline ice deforms slower than single crystalline ice, due to the stress being on the basal planes that are already blocked by other ice crystals. It ca... | Wikipedia - Mathematical geophysics | null | null | null |
Generally the ice has its linear elasticity constants averaged over one dimension of space to simplify the equations while still maintaining accuracy.Viscoelastic polycrystalline ice is considered to have low amounts of stress usually below one bar. This type of ice system is where one would test for creep or vibration... | Wikipedia - Mathematical geophysics | null | null | null |
Where it's a stress-strain relationship independent of time. This area is usually applied to transportation or building onto floating ice.Shallow-Ice approximation is useful for glaciers that have variable thickness, with a small amount of stress and variable velocity. One of the main goals of the mathematical work is ... | Wikipedia - Mathematical geophysics | null | null | null |
Mathematics in the Dewey Decimal Classification system Mathematics Subject Classification – alphanumerical classification scheme collaboratively produced by staff of and based on the coverage of the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH. | Wikipedia - Outline of mathematics | null | null | null |
Mathematics is divided into fields of Algebra, Geometry, Linear Algebra, Analytical Geometry, Mathematical Analysis, Probability, Statistics, Numerical Analysis, and Selected Chapters in Mathematics. | Wikipedia - Mathematical Grammar School | null | null | null |
Mathematics is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed. For example, any sequence of numbers that may be modeled by a mathematical function can be considered a pattern. Mathematics can be taught as a collection of patterns. | Wikipedia - Pattern | null | null | null |
Mathematics makes up that part of the human conceptual system that is special in the following way: It is precise, consistent, stable across time and human communities, symbolizable, calculable, generalizable, universally available, consistent within each of its subject matters, and effective as a general tool for desc... | Wikipedia - Where Mathematics Comes From | null | null | null |
Mathematics of general relativity Basic introduction to the mathematics of curved spacetime Tidal tensor Frame fields in general relativity | Wikipedia - Newtonian foundation of general relativity | null | null | null |
Mathematics programs initially developed in the 1990s that were based on the NCTM's Curriculum and Evaluation Standards for School Mathematics, like Core-Plus Mathematics, have been the subject of controversy due to their differences from more conventional mathematics programs. In the case of Core-Plus Mathematics, the... | Wikipedia - Core-Plus Mathematics Project | null | null | null |
For example, this debate led to some schools in Minnesota abandoning Core-Plus Mathematics in the early 2000s and returning to traditional mathematics curricula. In a master's degree research paper at the time, interviews with teachers at four schools that had dropped Core-Plus Mathematics suggested that many teachers ... | Wikipedia - Core-Plus Mathematics Project | null | null | null |
Mathematics, Art and Poetic Reflection, 2009-2010, premiered at the Bowery Poetry Club in New York City, New York. This exhibition consisted of nine shows, each show a month long typically featuring two artists or a small group. Featured poets or performers were invited to respond to the works with a performance at the... | Wikipedia - Rhythm of Structure | null | null | null |
The complete exhibition led to a published catalog and documentary film, which screened at the Sarasota Film Festival in 2012. The entire exhibition then traveled as a summary show to Ringling College of Art and Design, as well as Antioch College in 2011.Squares and Circles featuring John Hiigli and Vandorn Hinnant Thi... | Wikipedia - Rhythm of Structure | null | null | null |
Responding poems/poets: Quadrants by Kristin Prevallet, Images of Devonian Age by Pooh Kaye, and The Curvature of Green by Shanxing Wang.The Cartesian MathArt Hive featuring The Hive Artists The Cartesian MathArt Hive created by John Sims based on the rotations of his piece SquareRoots of a Tree in a collaboration of t... | Wikipedia - Rhythm of Structure | null | null | null |
Responding Poems/Poets:The Square Root of Love: Calculating the HEART of Things by JoAnne Growney, and Learning To Be My Father's Son or 16 Things I Could Never Tell My Father by Regie Cabico.John Sims' part of exhibition developed into a Valentine's Day wine-poetry-film project premiering in Paris in 2017.Selected Inf... | Wikipedia - Rhythm of Structure | null | null | null |
Responding Poems/Poets: 21 Reasons Why I hate Math by Shappy Seasholtz, and 29 Solutions For Writers, by People Who Know Better Than Me by Cristin O'Keefe Aptowicz.Mathematical Graffiti featuring Fernando Mora, John Sims with Kyle Goen, Mark Turgeon, and the Bowery Poetry Club Patrons Mathematical Graffiti featured: Fe... | Wikipedia - Rhythm of Structure | null | null | null |
Thomasino featured portions of this exhibition in his blog.The HyperQuilt featuring Helen Beamish, Elaine Ellison, Suzanne Gould, John Sims, Ella Toy, Diana Venters, and Paula Wynter The HyperQuilt featured: Helen Beamish, Elaine Ellison, Suzanne Gould, John Sims, Ella Toy, Diana Venters, and Paula Wynter. Responding P... | Wikipedia - Rhythm of Structure | null | null | null |
Mathematics, in the broadest sense, is just a synonym of formal science; but traditionally mathematics means more specifically the coalition of four areas: arithmetic, algebra, geometry, and analysis, which are, to some degree, the study of quantity, structure, space, and change respectively. | Wikipedia - Scientific discipline | null | null | null |
Mathematics1048 – 1131: Omar Khayyam. Persian mathematician and poet. "Gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections.". Extracted roots using the decimal system (the Indian numeral system). | Wikipedia - Timeline of science and engineering in the Muslim world | null | null | null |
MathematicsIbn al-Banna and al-Qalasadi used symbols for mathematics "and, although we do not know exactly when their use began, we know that symbols were used at least a century before this. "Astronomy and mathematicsIbn Masoud (Ghayyathuddin Jamshid ibn Mohamed ibn mas`oud, d. 1424 or 1436.) Wrote on the decimal syst... | Wikipedia - Timeline of science and engineering in the Muslim world | null | null | null |
Computed and observed the solar eclipses of 809AH, 810AH and 811AH, after being invited by Ulugh Beg, based in Samarqand to pursue his study of mathematics, astronomy and physics. His works include "The Key of arithmetics"; "Discoveries in mathematics"; "The Decimal point"; "the benefits of the zero". The contents of t... | Wikipedia - Timeline of science and engineering in the Muslim world | null | null | null |
MathematicsThe Arabic mathematician Mohammed Baqir Yazdi discovered the pair of amicable numbers 9,363,584 and 9,437,056 for which he is jointly credited with Descartes. | Wikipedia - Timeline of science and engineering in the Muslim world | null | null | null |
Mathieu functions play a role in certain quantum mechanical systems, particularly those with spatially periodic potentials such as the quantum pendulum and crystalline lattices. The modified Mathieu equation also arises when describing the quantum mechanics of singular potentials. For the particular singular potential ... | Wikipedia - Mathieu equation | null | null | null |
The transformation is achieved with the following substitutions y = r 1 / 2 φ , r = γ e z , γ = i g h , h 2 = i k g , h = e I π / 4 ( k g ) 1 / 2 . {\displaystyle y=r^{1/2}\varphi ,r=\gamma e^{z},\gamma ={\frac {ig}{h}},h^{2}=ikg,h=e^{I\pi /4}(kg)^{1/2}.} By solving the Schrödinger equation (for this particular potenti... | Wikipedia - Mathieu equation | null | null | null |
Mathomat is a trademark used for a plastic stencil developed in Australia by Craig Young in 1969, who originally worked as an engineering tradesperson in the Government Aircraft Factories (GAF) in Melbourne before retraining and working as head of mathematics in a secondary school in Melbourne. Young designed Mathomat ... | Wikipedia - Geometry template | null | null | null |
The first template was exhibited in 1970 at a mathematics conference in Melbourne along with a series of popular mathematics teaching lesson plan; it became an immediate success with a large number of schools specifying it as a required students purchase. As of 2017, the stencil is widely specified in Australian school... | Wikipedia - Geometry template | null | null | null |
Young also developed MathAid, which was initially produced by him when he was living in Ringwood, Victoria. He later sold the company. W&G published a series of teacher resource books for Mathomat authored by various teachers and academics who were interested in Mathomat as a teaching product. | Wikipedia - Geometry template | null | null | null |
Maths A covers more practical topics than Maths B and C, but it is still OP eligible. There are considerably fewer algebraic concepts in this subject, and it is suitable for students who either struggled with mathematics in Year 10, or who do not require a knowledge of abstract mathematics in the future. Maths A is des... | Wikipedia - Mathematics education in Australia | null | null | null |
The skills encountered are relevant to a vast array of careers (trade, technical, business etc.). Assessments in the subject include both formative and summative written tests, assignments and practical work. | Wikipedia - Mathematics education in Australia | null | null | null |
It is assessed in the categories: Knowledge & Procedures (KAPS); Modelling & Problem Solving (MAPS); Communication & Justification (CAJ). Although Maths A is not a pre-requisite subject, but it is sufficient for entrance to many tertiary courses.The course is divided into four semesters. The skills learned in each seme... | Wikipedia - Mathematics education in Australia | null | null | null |
Maths B is considerably more theoretical than Maths A, requiring advanced algebra skills to successfully complete. It is a common prerequisite for science and engineering courses at Queensland Universities. Maths B (in some schools) can be studied at the same time with either Maths A or Maths C, but not both. Maths B g... | Wikipedia - Mathematics education in Australia | null | null | null |
Assessments are similar as those of Maths A, which includes both formative (Semester 1) and summative (Semesters 2,3 and 4) written tests, assignments and post-assignment tests. It is also assessed in the three categories Knowledge & Procedures (KAP); Modelling & Problem Solving (MAP); Communication & Justification (CA... | Wikipedia - Mathematics education in Australia | null | null | null |
According to the Queensland Studies Authority, in 2010, 93% of students who studied Maths B were OP eligible. The course is divided into four (4) semesters. The skills learned each semester are as follows: Semester 1 (Year 11/Form 5): Functions (Linear, Quadratic, Absolute Value) Periodic Functions (Trigonometry, Sin/C... | Wikipedia - Mathematics education in Australia | null | null | null |
Maths C extends the topics taught in Maths B, and covers additional pure-maths topics (including complex numbers, matrices, vectors, further calculus and number theory). Although not necessarily more difficult, it must be studied in conjunction with Maths B. Maths C gives the students an understanding of the methods an... | Wikipedia - Mathematics education in Australia | null | null | null |
Maths C can be a pre-requisite to tertiary courses with a heavy maths/science basis. Some skills learned in Maths C would be found in business and economics degrees.The course is divided into four (4) semesters. The areas learned are in the following: Semester 1 (Year 11/Form 5): Real and Complex Numbers Matrices Vecto... | Wikipedia - Mathematics education in Australia | null | null | null |
Maths Year 2000 Scotland Maths Cymru (Wales) | Wikipedia - Count On | null | null | null |
Mating is initiated when up to five males follow closely behind a female and bite at her fins and body, possibly cued by pheromones indicating the female's readiness. Each male attempts to seize the female by engulfing one of her pectoral fins; at times two males might grasp a female on both sides simultaneously. Once ... | Wikipedia - Whitetip reef shark | null | null | null |
The male has a limited time in which to achieve copulation, as while he is holding the female's pectoral fin in his mouth he is being deprived of oxygen. On the other hand, if the female is willing, the pair settles side-by-side with their heads pressed against the bottom and their bodies at an upward angle.After a ges... | Wikipedia - Whitetip reef shark | null | null | null |
Parturition occurs from May to August (autumn and winter) in French Polynesia, in July (summer) off Enewetak Atoll, and in October (summer) off Australia. Females give birth while swimming, making violent twists and turns of their bodies; each pup takes under an hour to fully emerge. The newborns measure 52–60 cm (20–2... | Wikipedia - Whitetip reef shark | null | null | null |
This shark develops slowly compared to other requiem sharks; newborns grow at a rate of 16 cm (6.3 in) per year while adults grow as a rate of 2–4 cm (0.79–1.57 in) per year. Sexual maturity is reached at a length of around 1.1 m (3.6 ft) and an age of 8–9 years, though mature males as small as 95 cm (37 in) long have ... | Wikipedia - Whitetip reef shark | null | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.