Fr.: méthode d'Argelander
Friedrich Wilhelm Argelander (1799-1875), German astronomer. His most important work was his compilation of the Bonner Durchmusterung; → method.
raveš-e Bâdé-Veselink (#)
Fr.: méthode de Baade-Wesselink
A method used to determine the size of certain types of pulsating stars, including Cepheids, from their magnitude variations (photometry) and the corresponding radial velocities (spectroscopy).
Baade, from Walter (Wilhelm Heinrich) Baade (1893-1960), German/American astronomer, who made important contributions to the research on variable stars; Wesselink, from Adriaan J. Wesselink (1909-1995), Dutch/American astronomer, the originator of the method. → method.
Fr.: méthode de Biruni
A method devised by the Iranian astronomer Biruni (973-1048) to measure the Earth radius, using trigonometric calculations. In contrast to foregoing → Eratosthenes' method and → Mamun's method, which required expeditions to travel long distances, Biruni's method was on-site. He carried out the measurement when he was at Nandana Fort (at the southern end of the pass through the Salt Range, near Baghanwala in the Punjab). He first calculated the height of a hill (321.5 m). To do this he used the usual method of observing the summit from two places in a straight line from the hill top. He measured the distance, d, between the two places and the angles θ1 and θ2 to the hill top from the two points, respectively. He made both measurements using an astrolabe. The formula that relates these angles to the hill height is: h = (d. tan θ1 . tan θ2) / (tan θ2 - tan θ1). He then climbed to the hill top, where he measured the → dip angle (θ), that is the angle of the line of sight to the horizon. He applied the values he obtained for the dip angle and the hill's height to the following trigonometric formula to derive the Earth radius: R = h cosθ / (1 - cos θ). The result for the Earth radius was 12,851,369.845 cubits (or 6335.725 km, using favorable conversion units). Despite the fact that the method is very ingenious, such a precise value is only by chance, because of several drawbacks: The plane was not perfectly flat to serve as the smooth surface of the sea. A measuring instrument more accurate than the alleged 5 arc minutes was needed. And the method suffered from the → atmospheric refraction (See, e.g., Gomez, A. G., 2010, Journal of Scientific and Mathematical Research).
Abu Rayhân Mohammad Biruni (973-1048 A.D.), one of the greatest scholars of the medieval era, was an Iranian of the Khwarezm region; → method.
Fr.: méthode d'Eratosthène
A simple way of calculating the Earth's → circumference using two sticks and two theorems of the → Euclidean geometry. Eratosthenes calculated the length of a → meridian arc by measuring the shadow cast by a vertical → gnomon at noon on the → summer solstice. In Cyene (→ tropic of Cancer), no shadow is cast whereas in Alexandria, further north, the shadow is cast at an angle of 1/50 of 360° (measured using a → scaphe), or 7.2°, from the vertical. The circumference is therefore equal to 50 times the distance between the two cities. The distance from Syene to Alexandria was 5,000 stadia, which when multiplied by 50 gives the measure for the Earth's circumference, 250,000 stadia. Estimating the accuracy of this result is not easy because the unit of stadium is not uniquely defined in the ancient world. The most likely reconstruction puts Eratosthenes' stadium in the range 155-185m, implying an error of about 3% below or 15% above the true value. The modern value for the equatorial circumference of the Earth is 40,075 km. As scholars have pointed out, Eratosthenes' experiment was marred by several errors: Syene is not on the Tropic of cancer, it is not on the same meridian as Alexandria, and the distance between the two cities is less than he estimated. But the errors tended to cancel each other out, so his estimate was relatively accurate. See also: → Mamun's method, → Biruni's method.
Eratosthenes (c. 276-194 B.C.), Gk. mathematician, astronomer, and geographer. He studied in Athens and later became a librarian in Alexandria. His treatise On the Measuring of the Earth is lost. The account of his experiment has been preserved in Cleomedes (probably first century A.D.). See also → sieve of Eratosthenes; → experiment.
Fr.: méthode eulérienne
Fluid mechanics: A method in which the changes in the physical properties of the fluid, such as velocity, acceleration, and density are described at a fixed point in space occupied by the fluid. Compare with → Lagrangian method.
Fr.: méthode de Feautrier
One of the most successful general methods for the numerical solution of the → radiative transfer equation. This method has been primarily used to study → radiative transfer in the → photospheres of stars.
P. Feautrier (1964), C.r. hebd. Séanc. Acad. Sci. Paris 258, 3198; → method.
Fr.: méthode de Godunov
Suggested by Sergei K. Godunov (1929-) in 1959, Math. Sbornik, 47, 271, translated 1969, US Joint Publ. Res. Service, JPRS 7226; → method.
Fr.: méthode itérative
A method of computation in mathematics using → iteration.
Fr.: méthode lagrangienne
Fluid mechanics: An approach in which a single fluid particle (→ Lagrangian particle) is followed during its motion. The physical properties of the particle, such as velocity, acceleration, and density are described at each point and at each instant. Compare with → Eulerian method.
Fr.: méthod de Mamun
A method for deriving the Earth's size based on
measuring a length of meridian between two points corresponding
to the difference between the respective latitudes. The Abbasid caliph
al-Ma'mun (ruling from 813 to 833 A.D.), appointed two teams of surveyors to this
task. They departed from a place in the
desert of Sinjad (nineteen farsangs from Mosul and forty-three from
Samarra), heading north and south, respectively. They proceeded
until they found that the height of the Sun at noon had increased
(or decreased) by one degree compared to that for the starting point.
Knowing the variation of the Sun's → declination
due to its apparent → annual motion, they could relate
the length of the arc of meridian to the difference between the latitudes of
the two places.
They repeated the measurement a second time, and so found that the length of
one degree of latitude is somewhat between 56 and 57 Arabic miles (Biruni, Tahdid).
360 times this number yielded the Earth's circumference, and from it the radius
The seventh Abbasid caliph Abu Ja'far Abdullâh al-Ma'mûn, son of Hârûn al-Rashîd (786-833 A.D.); → method.
maximum entropy method (MEM)
raveš-e dargâšt-e bišiné
Fr.: méthode d'entropie maximum
A deconvolution algorithm which functions by minimizing a smoothness function in an image. The MEM seeks to extract as much information from a measurement as is justified by the data's signal-to-noise ratio.
A manner or mode of procedure, especially an orderly, logical, or systematic way of instruction, inquiry, investigation, experiment, and so on.
From M.Fr. méthode, from L. methodus "way of teaching or going," from Gk. methodus "scientific inquiry, method of inquiry," originally "following after," from → meta- "after" + hodos "way."
Raveš "mthod," originally "going, walking," from row "going," present stem of raftan "to go, walk;" Mid.Pers. raftan, raw-, Proto-Iranian *rab/f- "to go; to attack" + -eš a suffix of verbal nouns.
method of least squares
raveš-e kamtarin cârušhâ
Fr.: méthode des moindres carrés
A method of fitting a curve to data points so as to minimize the sum of the squares of the distances of the points from the curve.
method of small perturbations
raveš-e parturešhâ-ye kucak
Fr.: méthode des petites perturbations
The linearization of the appropriate equations governing a system by the assumption of a steady state, with departures from that steady state limited to small perturbations. Also called perturbation method.
method of successive approximations
raveš-e nazdinešhâ-ye payâpey
Fr.: méthode d'approximations successives
The solution of an equation or by proceeding from an initial approximation to a series of repeated trial solutions, each depending upon the immediately preceding approximation, in such a manner that the discrepancy between the newest estimated solution and the true solution is systematically reduced.
Monte Carlo Method
raveš-e Monte Carlo
Fr.: méthode de Monte Carlo
A computer-intensive technique that relies on repeated random sampling of a statistical population to compute its results. Monte Carlo simulation is often used for approximate numerical computations when application of strict methods requires too much calculation, or when it is infeasible or impossible to compute an exact result with a deterministic algorithm.
The term Monte Carlo was coined in the 1940s by physicists (Stanislaw Ulam, Enrico Fermi, John von Neumann, and Nicholas Metropolis) working on nuclear weapon projects in the Los Alamos National Laboratory. The name is a reference to a famous casino in Monaco which, it is said that, Ulam's uncle would borrow money to gamble at. → method.
Fr.: méthode de Newton
Same as the → Newton-Raphson method.
Fr.: méthode de Newton-Raphson
A method for finding roots of a → polynomial that makes explicit use of the → derivative of the function. It uses → iteration to continually improve the accuracy of the estimated root. If f(x) has a → simple root near xn then a closer estimate to the root is xn + 1 where xn + 1 = xn - f(xn)/f'(xn). The iteration begins with an initial estimate of the root, x0, and continues to find x1, x2, . . . until a suitably accurate estimate of the position of the root is obtained. Also called → Newton's method.
→ Newton found the method in 1671, but it was not actually published until 1736; Joseph Raphson (1648-1715), English mathematician, independently published the method in 1690.
Fr.: méthode de zéro
A method of comparing, or measuring, forces, electric currents, etc., by so opposing them that the pointer of an indicating apparatus remains at, or is brought to, zero, as contrasted with methods in which the deflection is observed directly. Same as zero method.
Fr.: méthode de perturbation
Approximate method of solving a difficult problem if the equations to be solved depart only slightly from those of a problem already solved.