Using these formulas, the area of any polygon can be found by dividing the polygon into triangles.

Using PET studies and word stimuli, Endel Tulving found that remembering is an automatic process.

Using the data collected by Vesto Slipher and his ( Hubble's ) assistant Milton Humason ( a former mule-driver and janitor ), Hubble and Humason found a direct relationship between a galaxy's distance and its relative speed away from the solar system.

Using mathematical rules and procedures based on properties of reducible configurations, Appel and Haken found an unavoidable set of reducible configurations, thus proving that a minimal counterexample to the four-color conjecture could not exist.

Using Huygens ' theory and the principle of superposition of waves, the complex amplitude at a further point P is found by summing the contributions from each point on the sphere of radius r < sub > 0 </ sub >.

Using a variety of specifications of the employment and unemployment equations ( using ordinary least squares vs. generalized least squares regression procedures, and linear vs. logarithmic specifications ), they found that a 10 percent increase in the minimum wage caused a 1 percent decrease in teenage employment, and no change in the teenage unemployment rate.

Using a 5-inch photographic camera, he manually examined over 200 three-hour exposures with a magnifying glass, and found no planets.

Using the techniques of differential calculus, the velocity and acceleration as a function of time can be found:

Using his theory, he discovered homologies showing that slightly changed body parts served different functions to meet new conditions, and he found an intermediate stage in the evolution of distinct sexes.

Using WordStar in " Nondocument Mode " was essentially the same as using a traditional text editor, but with more advanced text editing features than found in some mainframe-based editors.

Using dyes to test various plastics for leaks, they found a suitable plastic called Durex 1661½ which could be easily molded into a case.

Using these coefficients gives the Taylor polynomial of f. The Taylor polynomial of degree d is the polynomial of degree d which best approximates f, and its coefficients can be found by a generalization of the above formulas.

Using observations of the equinoxes and solstices, Hipparchus found that the length of the tropical year was 365 + 1 / 4 − 1 / 300 days, or 365. 24667 days ( Evans 1998, p. 209 ).

Using the Orient Express as a plot device came from two sources: Fleming had returned from the Istanbul conference in 1955 on the train, but found the experience drab, partly because there was no restaurant car.

Using self coloured thread enhances the sculptural nature of the stitches and enhances the details found in some of the intricate filling stitches.

Using only an unmarked straightedge and a compass, Greek mathematicians found means to divide a line into an arbitrary set of equal segments, to draw parallel lines, to bisect angles, to construct many polygons, and to construct squares of equal or twice the area of a given polygon.

Using knowledge passed from generation to generation and ingredients found in the wild near the abbey, the canons developed a unique ale, brewed only at the abbey.

Using flickr and blogs, several people engaged in ' Wondjina watching ', documenting the Wondjina graffiti they found.

Using Kramers ' law for the opacity it is found that

Using analysis of one nDNA and 2 mtDNA sequences, Moyle & Marks ( 2006 ) found one largely Asian lineage and one African group of greenbuls and bristlebills ; the Golden Greenbul seemes to be very distinct and form a group of its own.

Using recent data from a broader collection of countries, it was found that there is a positive link between GDP and well-being and no point at which wealthier countries ' subjective well-being ceases to increase.

Using a number of parameters to assess quality of life, Manchester University researchers found that typical anti-psychotics were no worse than atypical anti-psychotics.

Using meta data to index pages was found to be less than reliable, however, because the webmaster's choice of keywords in the meta tag could potentially be an inaccurate representation of the site's actual content.

Using MRI scans, Dr. Murray Stein, of the University of California, San Diego, found that when people with the disorder are shown pictures of angry faces, their amygdala-the brain's fear center-lights up with more activity than it does in people without the condition.

Using the Cartesian coordinate system, geometric shapes ( such as curves ) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape.

Using a trick, such as lying, to get possession of property is larceny.

Using Voyager 2 images, Kargel and Pozio ( 1996 ) characterized Harran Sulci as consisting of sinuous " mountainous ridges " 1-1. 5 km in height, and lying within relative topographic lows.

Using hundreds of FedEx boxes and materials that he " already had lying around " for shipping various items, Avila constructed every piece of furniture in his apartment.

Using a steering system that controlled the modified rocket's tail surfaces and wings equipped with ailerons, Fiedler was to land the missile on a skid especially bolted under the fuselage.

: Using * to denote a binary operation performed on a set

Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S < sup > n </ sup > → ℝ < sup > n </ sup > that does not equalize on any antipodes then we can construct a map g: S < sup > n </ sup > → S < sup > n-1 </ sup > by the formula

Using these tools, one can write a more complex text editor, and a simple compiler for a higher-level language and so on, until one can have a graphical IDE and an extremely high-level programming language.

Using pharmacogenomics, pharmaceutical companies can create drugs based on the proteins, enzymes and RNA molecules that are associated with specific genes and diseases.

Using the language of category theory, many areas of mathematical study can be cast into appropriate categories, such as the categories of all sets, groups, topologies, and so on.

Using ClearType on these display configurations will actually reduce the display quality.

Using to denote the size of the original grammar, the size blow-up in the worst case may range from to, depending on the transformation algorithm used.

Using pioneering film-looping technology, Enoch J. Rector presented the entirety of a famous 1897 prize-fight on cinema screens across the country.

* International Good Practice: Guidance on Project Appraisal Using Discounted Cash Flow, International Federation of Accountants, June 2008, ISBN 978-1-934779-39-2

Using the civil unrest in India as an excuse to move troops to the Durand Line, Afghan troops crossed the border at the western end of the Khyber Pass on 3 May 1919 and occupied the village of Bagh, the scene of an earlier uprising in April.

Using his favorite model in his last painting of her, a fellow painter, Victorine Meurent, also the model for Olympia and the Luncheon on the Grass, sits before an iron fence holding a sleeping puppy and an open book in her lap.

Using digital computers, on the other hand, both FIR and IIR filters are straightforward to implement in software.

Using humanist techniques for working on texts, he prepared important new Latin and Greek editions of the New Testament.

* Using Java, and based very closely on Weizenbaum's published description of the program: http :// www. chayden. net / eliza / Eliza. html

* Using Z80 assembly language on the TI-83 Plus: ticalc. org

Using this method, the customer does not need to authenticate his or her identity by PIN entry or signature, as on a regular machine.

Using FProxy, a user can browse freesites ( web sites that use normal HTML and related tools, but whose content is stored within Freenet rather than on a traditional web server ).

Using whatever equipment the vassal could obtain by virtue of the revenues from the fief, the vassal was responsible to answer calls to military service on behalf of the lord.

Using the submarine, Akatsuki, they hope to gather information on the robot's builders, the alien simians.

Using the notion of covering provided by a Grothendieck topology, it becomes possible to define sheaves on a category and their cohomology.

Using their data on the time occupied by travel to work, Table 2 below shows the absolute number of people who responded with travel times " at least 15 but less than 20 minutes " is higher than the numbers for the categories above and below it.

Using the Emergency-era Internal Security Act ( ISA ), the new government suspended Parliament and political parties, imposed press censorship and placed severe restrictions on political activity.