These concepts include one-to-one correspondence ( the basis of counting ), comparison to a standard ( used for measurement ), and the 3-4-5 right triangle ( a device for assuring a right angle ).

The notions of angle and distance become primitive concepts.

Diffeomorphism does not respect distance and angle, so these key concepts of Euclidean geometry are lost on a smooth manifold.

General vectors in this sense are fixed-size, ordered collections of items as in the case of Euclidean vectors, but the individual items may not be real numbers, and the normal Euclidean concepts of length, distance and angle may not be applicable.

Several other roots have similar normative and geometric descendants, such as Latin norma, whence norm, normal, and normative itself, and also geometric concepts such as normal vectors ; and likewise Greek ortho and Latin ordo, meaning either " right " or " correct " ( as in orthodox, meaning " correct opinion ") or " straight " or " perpendicular " ( as in orthogonal, meaning " perpendicular angle "), and thence order, ordinary, etc.

With these concepts, Pierre Wantzel ( 1837 ) proved that straightedge and compass alone cannot trisect an arbitrary angle nor double a cube, nor to construct a square equal in area to a given circle.

These additional challenges include such topics as exclusives and restrictive covenants, radius restrictions on near-by self-competition, co-tenancy, no-build areas and visibility corridors, parking ratio assurances, signage concerns ( including pylons, monuments, and criteria ), CAM and CAM caps and controls ( including the " cumulative " and " non-cumulative " concepts ), continuous operating covenants, and much more.

It contains a prequential evaluation method, the EDDM concept drift methods, a reader of ARFF real datasets, and artificial stream generators as SEA concepts, STAGGER, rotating hyperplane, random tree, and random radius based functions.

Relevant concepts: ( geodesic, exponential map, injectivity radius )

A borderline schizophrenic young man told me that to him the various theoretical concepts about which he had been expounding, in a most articulate fashion, during session after session with me, were like great cubes of almost tangibly solid matter up in the air above him ; ;

Although the Indian and Greek concepts of the atom were based purely on philosophy, modern science has retained the name coined by Democritus.

He also developed his own highly unusual theories of physics, according to which such concepts as " penetrability ", " suction and pressure " and " zig-zag-and-swirl " were discoveries on par with Einstein's Theory of Relativity.

With the rise of education, cheap newspapers and cheap printing, modern concepts of fame and celebrity began to develop, and the beneficiaries of this were not slow to cash in on this by producing autobiographies.

While the greatest players of the time, among them Alekhine, Emanuel Lasker and Capablanca, clearly did not allow their play to be hobbled by blind adherence to general concepts that the center had to be controlled by pawns, that development had to happen in support of this control, that rooks always belong on open files, that wing openings were unsound — core ideas of Tarrasch's chess philosophy as popularly understood — beginners were taught to think of these generalizations as unalterable principles.

Notable in his " system " were concepts such as overprotection of pieces and pawns under attack, control of the center by pieces instead of pawns, blockading of opposing pieces ( notably the passed pawns ) and prophylaxis.

During and after the First World War, these concepts were further developed by generals, such as Oskar von Hutier and the Reichswehr.

Following the First World War, these concepts were modified by the Reichswehr.

The concepts associated with the term blitzkrieg – deep penetrations by armour, large encirclements, and combined arms attacks – were largely dependent upon terrain and weather conditions.

But long before abstractions like the number arose, there were mathematical concepts to serve the purposes of civilization.

To offer an example of these concepts, O ' Flaherty makes use of " one of the oldest reasons why cities were built: military protection ".

However, although these early writers contributed greatly to the philosophical discovery of mind and this would ultimately lead to the development of psychology, they were working with an entirely different set of tools and core concepts than those of the cognitive scientist.

The essential concepts of the interpretation were devised by Niels Bohr, Werner Heisenberg and others in the years 1924 – 27.

By his view, concepts ( and ideas in general ) are innate ideas that were instantiations of a transcendental world of pure forms that lay behind the veil of the physical world.

The most important of the many elements of Cowboy Bebop were its sophisticated and mature existentialist and philosophical concepts.

The existing terms and structures available to them were often insufficient to express these new set of religious concepts, and taken together, these new forms of discourse led to the beginnings of Christology as an attempt to understand, explain and discuss their understanding of the nature of Christ.

Here, the apostle attempted to convey the underlying concepts about Christ to a Greek audience, and the sermon illustrates some key elements of future Christological discourses that were first brought forward by Paul.

These concepts were lost in the final production.

Alexander's mathematical concepts and orientation were similar to Edsger Dijkstra's influential A Discipline of Programming.

This meant to look at these concepts from the standpoint of the paradigm of critical psychology, thereby integrating their useful insights into critical psychology while at the same time identifying and criticizing their limiting implications while ( which in the case of S – R psychology were the rhetorical elimination of the subject and intentional action, and in the case of cognitive psychology which did take into account subjective motives and intentional actions, methodological individualism ).

Drawing from such concepts as the international scientific vocabulary and Standard Average European, linguists developed a theory that the modern Western languages were actually dialects of a hidden or latent language.

The concepts were highly influential, and his own contribution lives on in the names of the Hilbert class field and of the Hilbert symbol of local class field theory.

Stove alleged that by using weak or false ad hoc reasoning, these Ultra-Darwinists used evolutionary concepts to offer explanations that were not valid ( e. g., Stove suggested that sociobilogical explanation of altruism as an evolutionary feature was presented in such as way that the argument was effectively immune to any criticism.

The spoofs of I Love Lucy were supposed to be earlier concepts of the show that never made it on the air, such as " I Love Louie ", where Desi lived with Louis Armstrong.

Information Processing Language was the first AI language, from 1955 or 1956, and already included many of the concepts, such as list-processing and recursion, which came to be used in Lisp.

Following Plato, St. Augustine, for example, held the view that language was merely labels applied to already existing concepts, and this view remained prevalent throughout the Middle Ages.

Also, already during the interwar period, Otto Neurath and other members of the Vienna Circle strongly propagated the need for both the unity of science and the popularization of new scientific concepts.

* The U. S. Navy's s were described as " white elephants " because the " tactical and strategic concepts that inspired them were completely outmoded " by the time they were commissioned – the Japanese heavy cruisers that they were designed to hunt down had already been destroyed.

" Based on Heidegger's earliest lecture courses, in which Heidegger already engages Dilthey's thought prior to the period Gadamer mentions as " too late ", scholars as diverse as Theodore Kisiel and David Farrell Krell have argued for the importance of Diltheyan concepts and strategies in the formation of Heidegger's thought.

Due to the Department of Defense requiring as much of the syntax as possible to be based on Ada, in order to avoid re-inventing concepts that had already been thoroughly tested in the development of Ada, VHDL borrows heavily from the Ada programming language in both concepts and syntax.

However, in every respect, the concepts underlying the two systems are identical: in each, a new piece of information gets pegged to something that is already known.

that categorizes games by their form ( i. e. whether they are novel games proposed by the teacher or children, or whether they are existing games already widely played ), by the movement skills that they require, by the " movement concepts " and game tactics that they require, and by the educational results of the game.

Aristotle ( 384 – 322 BCE ) said definitions should describe the concept being defined in terms of other concepts already known.

In 1543, Nicolaus Copernicus had already posited that the planets orbited the Sun as the Earth does ; combined, these two concepts led to the thought that the planets might be " worlds " similar to the Earth.

Although most of its concepts had already been introduced elsewhere, it was the first camera to combine them all in one camera.

It can be argued, however, that there are already object-oriented concepts involved in the design of a more typical operating system such as Unix.

However, although the list of universities honored for their future concepts mostly consists of large and already respected institutions, the Federal Ministry of Education and Research claimed that the initiative was aimed at promoting universities with a dedicated future concept so they could continue researching on an international level.

NFL sources credit Rozelle with bringing concepts such as gate and television profit-sharing, policies already in place in the rival American Football League, to the NFL.

ABMA responded with a new design, the Juno V ( as a continuation of the Juno I and Juno II series of rockets, while Juno III and IV were unbuilt Atlas-and Titan-derived concepts ), which replaced the four E-1 engines with eight H-1s, a much more modest upgrade of the existing S-3D already used on the Thor and Jupiter missiles, raising thrust from 150, 000 to 188, 000 lbf ( 670 to 840 kN ).

He left to begin his own production company, Jonathan Goodson Productions, which produces both state lottery game shows and original game show concepts, with 2003's Dirty Rotten Cheater being the newest Goodson game, having already been sold internationally.

Some basic concepts such as identification and baseline ( well-defined point in the evolution of a project ) were already clear, but what was at stake was a set of techniques oriented towards the control of the activity, and using formal processes, documents, request forms, control boards etc.

But unlike the X-33 and other programs meant to replace the Shuttle, Constellation reused concepts already learned from the Apollo and Space Shuttle programs.

Although concepts with the names " complete " and " bounded " were already defined, confusion is unlikely to occur since one would rarely speak of a " bounded complete poset " when meaning a " bounded cpo " ( which is just a " cpo with greatest element ").

Agreeing with GameZone, Nintendo World Report called the game a masterpiece and the perfect example of how a Metroid game should be done: " The designers carefully mix all the best elements from the other games and layer them on top of the already brilliant level design and concepts of the original Metroid.

Beginning in 1989, the movement began naming everything connected to the Maharishi after him, even retroactively renaming already existing entities or concepts.

Although the exposition of Hindu doctrines to European audiences had already been attempted in piecemeal fashion at that time by many orientalists, Guénon ’ s Introduction to the Study of the Hindu Doctrines advanced its subject in a uniquely insightful manner, by referring to the concepts of metaphysics and Tradition in their most general sense, which Guénon precisely defined, along with the necessary distinctions and definitions of seemingly unambiguous terms such as religion, tradition, exoterism, esoterism and theology.

Novak's work is based on the cognitive theories of David Ausubel ( assimilation theory ), who stressed the importance of prior knowledge in being able to learn new concepts: " The most important single factor influencing learning is what the learner already knows.