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Congruence Principle (other)
Congruence may refer to: Mathematics * Congruence (geometry), being the same size and shape * Congruence or congruence relation, in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure * In modular arithmetic, having the same remainder when divided by a specified integer **Ramanujan's congruences, congruences for the partition function, , first discovered by Ramanujan in 1919 **Congruence subgroup, a subgroup defined by congruence conditions on the entries of a matrix group with integer entries **Congruence of squares, in number theory, a congruence commonly used in integer factorization algorithms * Matrix congruence, an equivalence relation between two matrices * Congruence (manifolds), in the theory of smooth manifolds, the set of integral curves defined by a nonvanishing vector field defined on the manifold * Congruence (general relativity), in general relativity, a congruence in a four-dimensional Lorentzian manifold that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Congruence (geometry)
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Therefore two distinct plane figures on a piece of paper are congruent if they can be cut out and then matched up completely. Turning the paper over is permitted. In elementary geometry the word ''congruent'' is often used as follows. The word ''equal'' is often used in place of ''congruent'' for these objects. *Two line segments are congruent if they have the same length. *Two angles are congruent if they have the same measure. *Two circles are congruent if they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solubility
In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubility of a substance in a specific solvent is generally measured as the concentration of the solute in a saturated solution, one in which no more solute can be dissolved. At this point, the two substances are said to be at the solubility equilibrium. For some solutes and solvents, there may be no such limit, in which case the two substances are said to be " miscible in all proportions" (or just "miscible"). The solute can be a solid, a liquid, or a gas, while the solvent is usually solid or liquid. Both may be pure substances, or may themselves be solutions. Gases are always miscible in all proportions, except in very extreme situations,J. de Swaan Arons and G. A. M. Diepen (1966): "Gas—Gas Equilibria". ''Journal of Chemical Physi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hatch Mark
Hatch marks (also called hash marks or tick marks) are a form of mathematical notation. They are used in three ways as: * Unit and value marks — as on a ruler or number line * Congruence notation in geometry — as on a geometric figure * Graphed points — as on a graph Hatch marks are frequently used as an abbreviation of some common units of measurement. In regard to distance, a single hatch mark indicates feet, and two hatch marks indicate inches. In regard to time, a single hatch mark indicates minutes, and two hatch marks indicate seconds. In geometry and trigonometry, such marks are used following an elevated circle to indicate degrees, minutes, and seconds — ( ° ) ( ′ ) ( ″ ). Hatch marks can probably be traced to hatching in art works, where the pattern of the hatch marks represents a unique tone or hue. Different patterns indicate different tones. Unit and value marks Unit-and-value hatch marks are short vertical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Congruence Principle (other)
The term congruence principle may refer to any undertaking that seeks to align apparently disparate things. Specifically, it may refer to: * In economics, the principle of fiscal equivalence, i.e., the false model in which the circle of buyers can be made to equate exactly with the circle of sellers. * In education, the notion that principles such as Bloom's Taxonomy assist in maintaining congruence among various educational undertakings. * In linguistics and etymology, the more contributing languages a linguistic feature exists in, the more likely it is to persist in the emerging language. See phono-semantic matching. * In mathematics, the application of principles associated with Cavalieri's principle. * In medicine, the corollary principle of metabolism that holds that "present-day metabolism holds traces of the primitive chemistry and could serve as a valuable source of inspiration in the elaboration of theories." * In psychology, a corollary to the principle of cognitive disson ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Congruence Bias
Congruence bias is the tendency of people to over-rely on testing their initial hypothesis (the most ''congruent'' one) while neglecting to test alternative hypotheses. That is, people rarely try experiments that could disprove their initial belief, but rather try to repeat their initial results. It is a special case of the confirmation bias. Examples Suppose that, in an experimental setting, a subject is presented with two buttons and told that pressing one of those buttons, but not the other, will open a door. The subject adopts the hypothesis that the button on the left opens the door in question. A direct test of this hypothesis would be pressing the button on the left; an indirect test would be pressing the button on the right. The latter is still a valid test because once the result of the door's remaining closed is found, the left button is proven to be the desired button. (This example is parallel to Bruner, Goodnow, and Austin's example in the psychology classic, '' A S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Humor
There are many theories of humor which attempt to explain what humor is, what social functions it serves, and what would be considered humorous. Among the prevailing types of theories that attempt to account for the existence of humor, there are psychological theories, the vast majority of which consider humor to be very healthy behavior; there are spiritual theories, which consider humor to be an inexplicable mystery, very much like a mystical experience. Although various classical theories of humor and laughter may be found, in contemporary academic literature, three theories of humor appear repeatedly: relief theory, superiority theory, and incongruity theory. Among current humor researchers, there is no consensus about which of these three theories of humor is most viable. Proponents of each one originally claimed their theory to be capable of explaining all cases of humor. However, they now acknowledge that although each theory generally covers its own area of focus, many in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mood Congruence
Mood congruence is the consistency between a person's emotional state with the broader situations and circumstances being experienced by the persons at that time. By contrast, mood incongruence occurs when the individual's reactions or emotional state appear to be in conflict with the situation. In the context of psychosis, hallucinations and delusions may be considered mood congruent (such as feelings of personal inadequacy, guilt, or worthlessness during a bipolar disorder depressive episode) or incongruent. Background and theorists An important consideration to the difference between mood congruence and mood dependent (or state-dependent) memory is the determination that one cannot make accurate assumptions about the emotional state of a memory during the encoding process. Therefore, the memory that is recalled is not dependent on the affective state during encoding. Another important difference is that there are multiple memories that can be recalled while in particular mood s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Rogers
Carl Ransom Rogers (January 8, 1902 – February 4, 1987) was an American psychologist and among the founders of the humanistic approach (and client-centered approach) in psychology. Rogers is widely considered one of the founding fathers of psychotherapy research and was honored for his pioneering research with the Award for Distinguished Scientific Contributions by the American Psychological Association (APA) in 1956. The person-centered approach, Rogers's unique approach to understanding personality and human relationships, found wide application in various domains, such as psychotherapy and counseling ( client-centered therapy), education ( student-centered learning), organizations, and other group settings. For his professional work he received the Award for Distinguished Professional Contributions to Psychology from the APA in 1972. In a study by Steven J. Haggbloom and colleagues using six criteria such as citations and recognition, Rogers was found to be the sixth most ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incongruent Transition
Incongruent transition, in chemistry, is a mass transition between two phases which involves a change in chemical composition. This is contrasted with congruent transition, for which the composition remains the same. The transition may be that of melting, vaporization or allotropism. The concept is also often extended to related phenomena, for example, incongruent dissolution of a solid by a liquid solvent, which is often encountered in geology Geology () is a branch of natural science concerned with Earth and other Astronomical object, astronomical objects, the features or rock (geology), rocks of which it is composed, and the processes by which they change over time. Modern geology .... The term "phase decomposition" is sometimes used to describe incongruent transition. However, it has to be kept in mind that incongruent transition is described by an equilibrium. For an example, see incongruent melting. References * {{refend Physical chemistry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Congruent Melting
Congruent melting occurs during melting of a compound when the composition of the liquid that forms is the same as the composition of the solid. It can be contrasted with incongruent melting. This generally happens in two-component systems. To take a general case, let A and B be the two components and AB a stable solid compound formed by their chemical combination. If we draw a phase diagram for the system, we notice that there are three solid phases, namely A, B and compound AB. Accordingly, there will be three fusion or freezing point curves AC, BE and CDE for the three solid phases. In the phase diagram, we can notice that the top point D of the phase diagram is the congruent melting point of the compound AB because the solid and liquid phases now have the same composition. Evidently, at this temperature, the two-component system has become a one-component system because both solid and liquid phases contains only the compound AB.Atkins' Physical Chemistry, 8th edition, by Peter A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scissors Congruence
The third of Hilbert's list of mathematical problems, presented in 1900, was the first to be solved. The problem is related to the following question: given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces which can be reassembled to yield the second? Based on earlier writings by Carl Friedrich Gauss, David Hilbert conjectured that this is not always possible. This was confirmed within the year by his student Max Dehn, who proved that the answer in general is "no" by producing a counterexample. The answer for the analogous question about polygons in 2 dimensions is "yes" and had been known for a long time; this is the Wallace–Bolyai–Gerwien theorem. Unknown to Hilbert and Dehn, Hilbert's third problem was also proposed independently by Władysław Kretkowski for a math contest of 1882 by the Academy of Arts and Sciences of Kraków, and was solved by Ludwik Antoni Birkenmajer with a different method than Dehn. Birk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Congruence Relation
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes (or congruence classes) for the relation. Basic example The prototypical example of a congruence relation is congruence modulo n on the set of integers. For a given positive integer n, two integers a and b are called congruent modulo n, written : a \equiv b \pmod if a - b is divisible by n (or equivalently if a and b have the same remainder when divided by n). For example, 37 and 57 are congruent modulo 10, : 37 \equiv 57 \pmod since 37 - 57 = -20 is a multiple of 10, or equivalently since both 37 and 57 have a remainder of 7 when divided by 10. Congruence modulo n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
