An Etymological Dictionary of Astronomy and Astrophysics
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A probability density function, denoted χ², that gives the distribution of the sum of squares of k independent random variables, each being drawn from the normal distribution with zero mean and unit variance. The integer k is the number of degrees of freedom. The distribution has a positive skew; the skew is less with more degrees of freedom. As degrees of freedom increase, the chi-square distribution approaches a normal distribution. The most common application is chi-square tests for goodness of fit of an observed distribution to a theoretical one. If χ² = 0 the agreement is perfect.

Chi Gk. letter of alphabet; → square; → distribution.

Vâbâžeš, → distribution; do, → two.

A force law that applies to the → gravitational and → electromagnetic forces in which the magnitude of the force decreases in proportion to the inverse of the square of the → distance.

→ inverse; → square; → law.

Any statistical procedure that involves minimizing the sum of squared differences.

→ least; → square.

A → cross correlation technique for computing average profiles from thousands of → spectral lines simultaneously. The technique, first introduced by Donati et al. (1997, MNRAS 291,658), is based on several assumptions: additive → line profiles, wavelength independent → limb darkening, self-similar local profile shape, and weak → magnetic fields. Thus, unpolarized/polarized stellar spectra can indeed be seen as a line pattern → convolved with an average line profile. In this context, extracting this average line profile amounts to a linear → deconvolution problem. The method treats it as a matrix problem and look for the → least squares solution. In practice, LSD is very similar to most other cross-correlation techniques, though slightly more sophisticated in the sense that it cleans the cross-correlation profile from the autocorrelation profile of the line pattern. The technique is used to investigate the physical processes that take place in stellar atmospheres and that affect all spectral line profiles in a similar way. This includes the study of line profile variations (LPV) caused by orbital motion of the star and/or stellar surface inhomogeneities, for example. However, its widest application nowadays is the detection of weak magnetic fields in stars over the entire → H-R diagram based on → Stokes parameter V (→ circular polarization) observations (see also Tkachenko et al., 2013, A&A 560, A37 and references therein).

→ least; → square; → deconvolution.

A fit through data points using least squares.

→ least squares; → fit.

An n × n matrix in which every row, column, and diagonal add up to the same number.

→ magic; → square.

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; → least squares.

An → integer of the form n², where n is a → positive number. In other words, a → perfect power when k = 2.

→ perfect; → square.

The square root of the arithmetic mean of the squares of the numbers in a given set.

→ root; → mean; → square.

The square root of the second moment corresponding to the frequency function of a random variable.

→ root; → mean; → square; → error.

Statistics: The square root of the arithmetic mean of the squares of the deviation of observed values from their arithmetic mean.

→ root; → mean; → square; → deviation.

1) A rectangle having all four sides of equal length.
2) The second power of a quantity, expressed as a² = a × a, where a is the quantity. → inverse square law.

M.E., from O.Fr. esquire "a square, squareness," from V.L. *exquadra, from *exquadrare "to square," from L. → ex- "out" + quadrare "make square," from quadrus "a square," from quattuor→ four.

Câruš, from Av. caθruša- "four sides (of a four-sided figure)", from caθru- "four," Mod.Pers. cahâr, câr "four" + uša- "angle," Mod.Pers. guš, gušé.

A solid angle whose cone is a tetrahedral pyramid with an angle between its edges equal to 1°. 1 square degree = 3.046 x 10^-4 sr = 2.424 x 10^-5 solid angle of a complete sphere.

→ square; → degree.

An international project to construct a highly sensitive radio interferometer array operating between 0.15 and 20 GHz with an effective collecting area of one square kilometer. The number of individual telescopes will be 2000 to 3000. SKA will have a sensitivity 100 times higher than that of today's best radio telescopes and an angular resolution < 0.1 arcsec at 1.4 GHz. The site will be selected in 2012 and early science with Phase 1 is scheduled for from 2016 on. See also the SKA homepage.

→ square; → kilometer; → array.

A → matrix with equal numbers of → rows and → columns (i.e., an n × n matrix).

→ square; → matrix.

A large → asterism of four stars, approximately square in shape, in the northern sky. Three of the stars, → → Markab, → Scheat, and → Algenib, belong to the constellation → Pegasus. The fourth, → Alpheratz, was lost to Pegasus when the constellation boundaries were formalised, and now lies just within the borders of → Andromeda.

→ square; → Pegasus.

Chahârguš, → tetragon; → Pegasus.

Quantity which when multiplied by itself produces another quantity.

→ square; → root.

An oscillation which alternatively assumes, for equal lengths of time, one or two fixed values.

→ square; → wave.

The mathematical problem of subdividing a square into a number of smaller squares, all of different sizes.

→ square; → square.