By dividing the board into smaller pieces, constructing tours on each piece, and patching the pieces together, one can construct tours on most rectangular boards in polynomial time.

By 1830, probably inspired by his neighbor Freeman Thomas's Grand Tunnel coal mine, Harvey supplemented his farm income by constructing a coal tunnel.

By constructing the splitting field for such a polynomial one can find the roots of the polynomial in the new field.

By constructing a valid model for a subsystem without a specific axiom, we show that the omitted axiom is independent if its correctness does not necessarily follow from the subsystem.

By constructing artificial intelligence systems that have structural features similar to those of humans, we may be more likely to achieve human-like functionality.

By constructing the Wehnelt cylinder such that it has a higher negative charge than the filament itself, electrons that exit the filament in a diverging manner are, under proper operation, forced into a converging pattern the minimum size of which is the gun crossover diameter.

By transforming the process of media consumption into an active and critical process, people gain greater awareness of the potential for misrepresentation and manipulation ( especially through commercials and public relations techniques ), and understand the role of mass media and participatory media in constructing views of reality.

By constructing a situation in which the electrostatic potential varies for two paths of a particle, through regions of zero electric field, an observable Aharonov – Bohm interference phenomenon from the phase shift has been predicted ; again, the absence of an electric field means that, classically, there would be no effect.

By that time, most frontier communities already had barns and those that did not were constructing them using hired labor.

By constructing different combinations of 5-sided and 6-sided rings, vesicles of different sizes may assemble.

By the time the models entered production, Renault had assigned more than 500 people to the project, logging 14, 500, 000 hours of study and testing, constructing 44 prototypes, testing 130 engines, and test-driving prototypes more than 2. 2 million km.

By granting the patent holder the exclusive right, privilege and liberty of making, constructing, using, and selling the invention, the patent act establishes that any other person making, constructing, using, or selling the patented invention is infringing that patent.

By constructing a fake web site that looks like a legitimate site that might ask for the user's personal information, such as a copy of a bank's website, the fraudster can " phish ", or steal by means of false pretenses, a victim's passwords, PIN or bank account number.

By 1913, however, the House had outgrown the available office space, and fifty-one rooms were added to the original structure by raising the roof and constructing a fifth floor that is visible only from the enclosed court.

By 1950, Birmingham City Council had been constructing municipal housing to accommodate the rising population of Birmingham and to accommodate those who had been displaced by the slum clearances in the inner-city areas of the city, similar to the process which had started some 30 years earlier when the first council houses were built.

By 1962, however, the city council was demolishing more houses than it was constructing and Fidler urged the council to adopt the French Camus system which consisted of housing at a density of approximately 50 houses per hectare and 80 people per acre.

By the end of the 1970s, this plant became the major centre for designing, constructing, manufacturing, testing and deploying strategic and space missile complexes in the Soviet Union.

By class field theory, this can only be true if there is an unramified extension of the field of pth roots of unity by a cyclic extension of degree p which behaves in the specified way under the action of Σ ; Ribet proves this by actually constructing such an extension using methods in the theory of modular forms.

By constructing a potentially solipsistic world of privately-constructed virtual realities, Schroeder is able again to create ambiguities in the relationship of subject to object that undermine both categories.

By constructing null models to test the data against ( as in Doak et al.

By utilizing the hydroelectric potential of the Inga Dam and by constructing one switching station near Kinshasa at Selo, the Government of Zaire under Mobutu Sese Seko was theoretically able to control the flow of power to secession-prone Katanga, then Shaba, province, but never actually exercised this option.

By mixing uses ( retail, office, and residential ), constructing a through-block arcade ( connecting to the IBM building to the east ), and using the air rights from Tiffany ’ s flagship store next door, and including the atrium ( designed as a “ public space ” under the city codes at the time ), Trump was able to assemble a bonus package that enabled a taller tower.

By the latter half of the 19th century constructing wind driven whirligigs had become a pastime and art form.

By performing the same experiment over and over again, he discovered that ice always melted at the same calibration mark on the thermometer.

By calibration and calculation, these measured quantities can lead to a measurement of humidity.

By determining the retention volumes ( or times ) of monodisperse polymer standards ( e. g. solutions of monodispersed polystyrene in THF ), a calibration curve can be obtained by plotting the logarithm of the molecular weight versus the retention time or volume.

By 1961 the radio-interferometer calibration techniques developed for the spectroheliograph first allowed an antenna system, with 52 " fan beam, to equal the angular resolution of the human eye in one observation.

By ( 1 ), the image of this pencil is a ruled surface of order Af which is met by the plane of the pencil in a curve, C, of order Af.

By varying the formula, this curve may be moved forward or backward along the coordinates to produce any desired compression strength / density ratio.

By banking the curve, the force exerted upon the car in a direction normal to the road surface has a horizontal component that provides this centripetal force.

By choosing the angle of bank to match the car's speed around the curve, the car seat transmits only a perpendicular force to the passengers, and the passengers no longer feel a need to lean nor feel a sideways push by the car seats or doors.

By construction, each point on the curve shows productive efficiency in maximizing output for given total inputs.

By looking at the place where the sun shadow from the rod falls on a carved curve, a navigator is able to sail along a line of latitude.

By moving the two points closer together so that Δy and Δx decrease, the secant line more closely approximates a tangent line to the curve, and as such the slope of the secant approaches that of the tangent.

By its very nature, conceptualizing a supply curve requires that the firm be a perfect competitor — that is, that the firm has no influence over the market price.

By its very nature, conceptualizing a demand curve requires that the purchaser be a perfect competitor — that is, that the purchaser has no influence over the market price.

By geometrical methods which were an early use of calculus, he showed that this curve is a cycloid, not the circular arc of a pendulum's bob, so pendulums are not isochronous.

By combining light curve data with observed spectral changes, astronomers are often able to explain why a particular star is variable.

By observing and recording the animals ’ escapes and escape times, Thorndike was able to graph the times it took for the animals in each trial to escape, which eventually resulted in a learning curve.

By conservation of energy the speed of motion of the body along an arbitrary curve does not depend on the horizontal displacement.

By removing the γu term, a regular Bézier curve results.

By varying the line frequency with an inverter, induction motors can be kept on the stable part of the torque curve above the peak over a wide range of rotation speeds.

By evaluating a Bézier or a NURBS curve at various values of the parameter, the curve can be represented in Cartesian two-or three-dimensional space.

By definition, each point on the curve is productively efficient, but, given the nature of market demand, some points will be more profitable than others.

By contrast, lack of competition in a market creates a downward sloping demand curve for a monopolist or oligopolist: although they will lose some business by raising prices, they will not lose it all, and it may be more profitable in most situations to sell at a higher price.

By contrast, the point z < sub > 0 </ sub > is called a logarithmic branch point if it is impossible to return to the original function element by analytic continuation along a curve with nonzero winding number about z < sub > 0 </ sub >.

</ li >< li > By projecting onto of a curve one can calculate

By varying the weighting parameter b, one can trace out the entire contract curve: If b

By the isoperimetric inequality and Barbier's theorem, the circle has the maximum area of any curve of given constant width.