An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

There are only three parameters that can be applied by an outside observer relating to a → black hole: → mass, → electric charge, and → angular momentum. The collapse of a star into a black hole wipes out all other details of its structure, and the observer can never discover any other properties of the star which formed the black hole. In other words, none of its characteristics leave any trace outside the black hole, and that is what is meant by "hair."

No, M.E., from O.E. na "never, no," cognate with Pers. na, nâ, → non-; → hair; → theorem.

Farbin, → theorem; bimuyi, noun from bimu "without hair," from bi- "without" (→ in-) + mu, → hair.
Kacali "baldness," from kacal "bald," also "crooked, bandy-legged," from kajal, from kaj "crooked, curved, bent" + → -al; probably unrelated to kal "bald," → colure.

A → symmetry in a physical system leads to a → conserved quantity. For example, symmetry under → translation corresponds to conservation of → momentum, symmetry under → rotation to conservation of → angular momentum, and symmetry in → time to conservation of → energy. The Noether symmetry theorem is a fundamental tool of modern theoretical physics and the calculus of variations, allowing to derive conserved quantities from the existence of variational symmetries.

Named in honor of the German-American woman mathematician Amalie Emmy Noether (1182-1935), who published the theorem in 1918 ("Invariante Variationsprobleme," Nachr. D. König. Gesellsch. D. Wiss. Zu Göttingen, Math-phys. Klasse 1918: 235-257).

The minimum number of resolution elements required to properly sample a signal, such as a star image, without causing erroneous effects known as aliasing. For electronic imaging, this number is generally taken as 2 pixels across the seeing disk diameter at the half intensity points. Also called → Shannon's sampling theorem and → sampling theorem.

Named after Harry Nyquist (1889-1976), a Swedish-born American physicist, who made important contributions to information theory, and Claude Elwood Shannon (1916-2001), an American mathematician and pioneer of information theory; → theorem.

The → moment of inertia of a body about any given axis is the moment of inertia about a parallel axis through the center of mass, plus the moment of inertia about the given axis if the mass were located at the center of mass. same as → Steiner's theorem.

→ parallel; → axis; → theorem.

A theorem relating the → Fourier coefficients to the function that they describe. It states that: (1/L) ∫ |f(x)|²dx (integrated from x₀ to x₀ + L) = (a₀/2)² + (1/2) Σ (a_r² + b_r²) (summed from r = 1 to ∞). In other words, the sum of the moduli squared of the complex Fourier coefficients is equal to the average value of |f(x)|² over one period.

Named after Marc-Antoine Parseval (1755-1836), French mathematician; → theorem.

A collapsing object whose radius is less than its Schwarzschild radius must collapse into a singularity.

→ Penrose process; → theorem.

The → moment of inertia of a plane object (→ lamina) about an axis perpendicular to the plane is equal to the sum of the moments of inertia about any two perpendicular axes in the plane. Thus if x and y axes are in the plane, I_z = I_x + I_y.

→ perpendicular; → axis; → theorem.

In an → isolated system, any initial state will occur again in the course of the → evolution of the system over a sufficiently long but finite → time.

→ Poincaré sphere; → recurrence; → theorem.

The space through which electromagnetic radiation passes is filled with electric and magnetic fields at right angles to each other and to the direction of propagation of the radiation. The rate of energy transfer is given by the Poynting vector.

In honor of John Henry Poynting (1852-1914), English physicist; → theorem.

The proposition that the → square of the → hypotenuse of a → right triangle is equal to the → sum of the squares of the other two sides: a² + b² = c².

After Pythagoras (c570 BC-c495BC), Greek philosopher and mathematician; → theorem.

1) General: Any theorem that expresses various reciprocal relations for the behavior of some physical systems, in which input and output can be interchanged without altering the response of the system to a given excitation.
2) In classical electromagnetism, the theorem stating that the current in a detector divided by the voltage at the source remains constant when source and detector are interchanged, as long as the frequency and all the impedances are left unchanged.

Reciprocity, from L. reciproc(us) "returning the same way, alternating" + → -ity; → theorem.

Farbin, → theorem; dosuyegi, quality noun of dosuyé nuanced term of dosu "two-sided," from do, → two, + su "direction, side," from Mid.Pers. sôk "direction, side."

The theorem stating that the value of the line integral of a complex function, taken along a simple closed curve encircling a finite number of isolated singularities, is given by 2πi times the sum of the residues of the function at each of the singularities.

→ residue; → theorem.

If a function f(x) is → continuous on an interval [a,b] and is → differentiable at all points within this interval, and vanishes at the end points x = a and x = b, that is f(a) = f(b) = 0, then inside [a,b] there exists at least one point x = c, a < c < b, at which the derivative f'(x) vanishes.

Named after Michel Rolle (1652-1719), a French mathematician; → theorem.

A uniqueness theorem involving the equations of state of stellar structure. → Vogt-Russell theorem.

Named after the German astronomer Heinrich Vogt (1890-1968) and the American astronomer Henry Norris Russell (1877-1957); → theorem.

Same as → Nyquist-Shannon sampling theorem.

→ sampling; → theorem.

Same as → sampling theorem.

→ Shannon entropy; → sampling; → theorem.

The → moment of inertia of a body about an arbitrary axis x' is equal to the sum of its moment of inertia about axis x, passing through the center of mass of the body and parallel to axis x', and the product of the mass M of the body by the square of the distance d between axes x and x': I_x' = I_x + Md². Same as → parallel axis theorem.

Named after Jakop Steiner (1796-1863), a Swiss mathematician who derived this statement; → theorem.

In a rapidly rotating fluid, the fluid velocity is constant along any line parallel to the axis of rotation.

→ Taylor number; Joseph Proudman (1888-1975), British mathematician and oceanographer.

A → proposition, → statement, or → formula in → mathematics or → logic deduced from → axioms, other propositions, → assumptions, → premises, or formulas. Theorems are statements which can be proved. For example, → Fourier theorem; → Liouville's theorem; → Woltjer's theorem.

From M.Fr. théorème, from L.L. theorema, from Gk. theorema "spectacle, speculation," in Euclid "proposition to be proved," from theorein "to look at, speculate, consider."

Farbin, from far- intensive prefix "much, abundant; elegantly; forward" (Mid.Pers. fra- "forward, before; much; around;" O.Pers. fra- "forward, forth;" Av. frā, fərā-, fra- "forward, forth; excessive;" cf. Skt. prá- "before; forward, in front;" Gk. pro "before, in front of;" L. pro "on behalf of, in place of, before, for;" PIE *pro-) + bin, present stem of didan "to see," from Mid.Pers. wyn-; O.Pers. vain- "to see;" Av. vaēn- "to see;" cf. Skt. veda "I know;" Gk. oida "I know," idein "to see;" L. videre "to see;" PIE base *weid- "to know, to see."

1) Physics: A → potential that satisfies both → Poisson's equation and the → boundary conditions pertinent to a particular field is the only possible potential.
2) Math.: If two → continuous functions φ(t) and ψ(t) have one and the same → Laplace transform F(p), then these functions are identically equal.
3) Astro.: A → black hole can only be characterized by its → mass, → electric charge, and → angular momentum. See also → no hair theorem.

→ uniqueness; → theorem.