While firing a higher quantity of smaller bullets makes it easier to hit a target ( and is therefore good for beginner marksmen ), it offers very little to more advanced marksmen.

Silvermintz notes that, " Historians of economic thought credit Plato, primarily on account of arguments advanced in his Republic, as an early proponent of the division of labor .” Notwithstanding this, Silvermintz argues that, " While Plato recognizes both the economic and political benefits of the division of labor, he ultimately critiques this form of economic arrangement insofar as it hinders the individual from ordering his own soul by cultivating acquisitive motives over prudence and reason.

While at the basic levels, meditation is geared toward relaxation, the practice of advanced meditators may be aimed toward the purpose of dividing one from their awareness of " self ," to a certain degree, and for a certain time.

While even many tribal cultures are losing traditional folk music and folk cultures, the process is most advanced " where industrialization and commercialisation of culture are most advanced ".

While technologically and culturally the city dwellers were more advanced, they could do little militarily to defend against the mounted hordes of the steppe.

While it was technically possible to retrofit more advanced floppy drives such as the high-density drive ( released in 1984 ) into the original IBM PC, this was not an option offered by IBM for the 5150 model, and the move to high-density 5. 25-inch floppies in particular was notoriously fraught with disk compatibility problems.

While in Baltimore the team advanced to the postseason ten times and won three NFL Championship games in 1958, 1959 and 1968.

While at General Electric, from 1909 – 1950, Langmuir advanced several basic fields of physics and chemistry, invented the gas-filled incandescent lamp, the hydrogen welding technique, and was awarded the 1932 Nobel Prize in Chemistry for his work in surface chemistry.

While an ' arm lead ' without the transfer of weight ( or movement of the body ) on the part of the leader is often a marker of an inexperienced or poorly taught dancer, the process of leading and following, particularly at an advanced level, often involves the contra-and contrasting uses of weight transfers and ' arm moves '.

While heavy machine guns such as the Maxim gun and the Vickers gun were fearsome defensive weapons in a built-up emplacement, they were very hard to move to a new position if the army had advanced to a new area, or if it had to fall back.

While the army held more than its own against the armies of the kingdom's neighbors, its performance against more technologically advanced European armies deteriorated over time.

While more powerful and with seemingly more advanced graphics, the Virtual Boy was not intended to replace the Game Boy in Nintendo's product line, as use of the system requires a steady surface and completely blocks the player's peripheral vision.

While automobile engine technology had remained fairly stagnant in World War II, advanced aircraft piston engine development had provided a great deal of available data, and NASCAR was formed just as some the improved technology was about to become available in production cars.

While a simple scalar treatment of the moment of inertia suffices for many situations, a more advanced tensor treatment allows the analysis of such complicated systems as spinning tops and gyroscopic motion.

While Stephen and his army besieged Lincoln Castle at the start of 1141, Robert of Gloucester and Ranulf of Chester advanced on the king's position with a somewhat larger force.

While international trade has been present throughout much of history ( see Silk Road, Amber Road ), its economic, social, and political importance have increased in recent centuries, mainly because of Industrialization, advanced transportation, globalization, multinational corporations, and outsourcing.

While arms and ammunition stores were found, there were no traces of the advanced facilities claimed to exist.

While many websites send additional information in a 404 error message — such as a link to the homepage of a website or a search box — there are also much more advanced extensions available as widgets that endeavor to find the correct web page the user wanted.

While fire and forget missiles have definitive advantages in terms of guidance and operator safety, and include abilities such as top attack mode, older missiles continue in use, both in the front line armies of less developed countries, and in reserve service the world over, due to their lower cost or existing stockpiles of less advanced weapons.

While initially profitable, the mining generally ended because the deeper reefs contained not only gold but other metals, and mining technology at the time was not advanced enough to cope with these and extract the gold profitably.

While the Amiga had the benefit of some rather advanced hardware for the time coders on the ST had to make do with a marginally faster clock-speed and later on abusing the hardware to do certain tricks like emulating hardware scrolling.

While an active license is not required to take advanced provider courses such as PALS, NRP, or ACLS, the practice of skills taught must have an accompanied license.

While arcade systems such as the Sega Model 3 remained more advanced than home systems, consoles and computers began approaching technological parity with arcade equipment.

While EIGRP is indeed an advanced distance-vector routing protocol, it is not a hybrid protocol.

While not publishing mathematical research in conventional ways during the 1980s, he produced several influential manuscripts with limited distribution, with both mathematical and biographical content.

While in normal typography these are just alternate font variants, they may have different meanings as mathematical symbols.

While some of Euler's proofs are not acceptable by modern standards of mathematical rigour ( in particular his reliance on the principle of the generality of algebra ), his ideas led to many great advances.

While the patent was initially rejected by the patent office as being a purely mathematical invention, following 12 years of appeals, Pardo and Landau won a landmark court case at the CCPA ( Predecessor Court of the Federal Circuit ) overturning the Patent Office in 1983 — establishing that " something does not cease to become patentable merely because the point of novelty is in an algorithm.

While areas of many simple surfaces have been known since antiquity, a rigorous mathematical definition of the area requires a lot of care.

While other such approaches have been developed, those based on moments are advantageous in terms of mathematical and computational simplicity.

While these result in some contradictions and lack completeness in a mathematical sense ( being based on axioms that are " merely " self-evident, but not robust under the stresses of radical scepticism ), the paradoxes can nonetheless be analysed rationally using the subatomic applications of quantum cosmology-particularly through the employment of the Schrödinger wave equations.

While Lobachevsky created a non-Euclidean geometry by negating the parallel postulate, Bolyai worked out a geometry where both the Euclidean and the hyperbolic geometry are possible depending on a parameter k. Bolyai ends his work by mentioning that it is not possible to decide through mathematical reasoning alone if the geometry of the physical universe is Euclidean or non-Euclidean ; this is a task for the physical sciences.

While it is often assumed that those with this intelligence naturally excel in mathematics, chess, computer programming and other logical or numerical activities, a more accurate definition places less emphasis on traditional mathematical ability and more on reasoning capabilities, recognizing abstract patterns, scientific thinking and investigation and the ability to perform complex calculations.

While Bolzano had developed a reasonably rigorous definition of a limit as early as 1817 ( and possibly even earlier ) his work remained unknown to most of the mathematical community until years later,

While Hilbert's tenth problem is not a formal mathematical statement as such the nearly universal acceptance of the ( philosophical ) identification of a decision algorithm with a total computable predicate allows us to use the MRDP theorem to conclude the tenth problem is unsolvable.

While the complexity of real food webs connections are difficult to decipher, ecologists have found mathematical models on networks an invaluable tool for gaining insight into the structure, stability, and laws of food web behaviours relative to observable outcomes.

While the theorems of Gödel and Gentzen are now well understood by the mathematical logic community, no consensus has formed on whether ( or in what way ) these theorems answer Hilbert's second problem.

While infinitesimals eventually disappeared from the calculus, their mathematical study continued through the work of Levi-Civita and others, throughout the late nineteenth and the twentieth centuries, as documented by Philip Ehrlich ( 2006 ).

While the mathematical probability of an event has a value in the range from zero to one, " the odds " in favor of that same event lie between zero and infinity.

While they have useful mathematical properties, they can produce counter-intuitive results: an event with an 80 % probability of occurring is four times more likely to happen than an event with a 20 % probability, but the odds are 16 times higher on the less likely event ( 4 – 1 against, or 4 ) than on the more likely one ( 1 – 4, or 4 – 1 on, or 0. 25 ).

While some coders specialize in developing system-level functionality ( such as providing wrappers and APIs for other coders to base their code on ), others code effects which are usually visual representations of mathematical formulas, such as fractals or metaballs.

" While Javits said any government official who sought to use the bill for busing purposes " would be making a fool of himself ," two years later the Department of Health, Education and Welfare said that Southern school districts would be required to meet mathematical ratios of students by busing.

While admitting that it made him " a little sore ", Patrick has said that the research he and his students conducted was seminal in developing mathematical models against which further research could be compared.

While complex problems can be broken down into simpler multiplications, the answers to these basic operations themselves are essential for more complex mathematical operations.

While content validity depends on a theoretical basis for assuming if a test is assessing all domains of a certain criterion ( e. g. does assessing addition skills yield in a good measure for mathematical skills?

While this was a little outside the main centres of British mathematical research, Burnside remained a very active researcher, publishing more than 150 papers in his career.

While possibly following Pythagorean modes of thinking, Vincenzo is known to have discovered a new mathematical relationship between string tension and pitch, thus suggesting a generalization of the idea that music and musical instruments can be mathematically quantified and described.