An Etymological Dictionary of Astronomy and Astrophysics
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A mapping of an infinite → space-time onto a finite one that may make the far away parts of the former accessible to study. The technique invented by Penrose defines an equivalence class of → metrics, g_ab being equivalent to ĝ_ab = Ω²g_ab, where Ω is a positive scalar function of the space-time that modifies the distance scale making the asymptotics of the physical metric accessible to study.

→ conformal; → compactification.

A cosmological model developped by Roger Penrose and colleagues according which the Universe undergoes repeated cycles of expansion. Each cycle, referred to an aeon, starts from its own "→ big bang" and finally comes to a stage of accelerated expansion which continues indefinitely. There is no stage of contraction (to a "→ big crunch") in this model. Instead, each aeon of the universe, in a sense "forgets" how big it is, both at its big bang and in its very remote future where it becomes physically identical with the big bang of the next aeon, despite there being an infinite scale change involved, on passing from one aeon to the next. This model considers a conformal structure rather than a metric structure. Conformal structure may be viewed as family of metrics that are equivalent to one another via a scale change, which may vary from place to place. Thus, in conformal space-time geometry, there is not a particular metric g_ab, but an equivalence class of metrics where the metrics ğ_ab and g_ab are considered to be equivalent if there is a smooth positive scalar field Ω for which ğ_ab = Ω g_ab (R. Penrose, 2012, The Basic Ideas of Conformal Cyclic Cosmology).

→ conformal; → cyclic; → cosmology.

The study of the set of angle-preserving transformations on a space.

→ conformal; → geometry.

A continuous mapping u = f(x) of a domain D in an n-dimensional Euclidean space (n≥ 2) into the n-dimensional Euclidean space is called conformal at a point x₀∈ D if it has the properties of constancy of dilation and preservation of angles at this point.

→ conformal; → mapping.

A crucial period in the history of the → Universe, when the bulk of stars in massive galaxies were likely formed. Observations of young stars in distant galaxies at different times in the past have indicated that the → star formation rate peaked at the → redshift of z ~ 2, some 10 billion years ago, before declining by a factor of around ten to its present value (P. Madau & Dickinson, 2014, arXiv:1403.0007).

→ cosmic; → star; → formation; → peak.

1) To undergo → deformation.
2) To change the form or shape of. → deformable, → deformed, → deformation.

From O.Fr. déformer, from L. deformare "to disfigure," from → de- + → form.

Vâdisidan, vâdisândan infinitive from vâdis, from vâ-, → de-, + dis, → form.

Capable of being → deformed. → deformable mirror

→ deform + → -able.

A very thin mirror whose shape can be changed by the force applied by many small pistons behind the mirror. Such a mirror is used in the → adaptive optics technique to correct the → wavefront affected by the → atmospheric turbulence. See also → tip-tilt mirror.

→ deformable; → mirror.

Altering in the size or shape of a body. See also → deformable.

Verbal noun of → deform.

Having the → form → changed.

Past participle of → deform.

A formula that gives the position of an image formed by highly → paraxial rays from a → spherical mirror. It is quite accurately given by: 1/x_o + 1/x_i = 2/x_C, where x_o is the distance along the → principal axis from the mirror to the object, x_i is the distance from mirror to image, and x_C is the distance from the mirror to its center of curvature. Any distance measured on the same side of the mirror as the reflecting surface is positive; on the other side, negative. Thus for a → concave mirror  x_C is positive; for a → convex mirror, negative.

→ Descartes; → formula.

Symbolic representation of the definition of a physical quantity obtained from its units of measurement. For example, with M = mass, L = length, T = time, area = L², velocity = LT^-1, energy = ML²T^-2. → dimensional analysis.

→ dimensional; → formula.

A deformation of a → solid body in which the change (→ strain) in the relative position of points in the body disappears when the deforming stress is removed. See also → elastic limit.

→ elastic; → deformation.

1) In physics, a mathematical equation that predicts observed results, but has no known theoretical basis to explain why it works.
2) In chemistry, a simple expression of the relative number of each type of atom in a chemical compound.

→ empirical; → formula

A formula which expresses an → exponential function with an → imaginary number  → exponent in terms of → trigonometric functions:
e^iθ = cos θ + i sinθ,
e^-iθ = cos θ - i sinθ,
cosθ = (e^iθ + e^-iθ)/2,
sinθ = (e^iθ - e^-iθ)/2i.
In the particular case of θ = π, Euler's formula becomes: e^iπ + 1 = 0, which is considered by many mathematicians to be the most elegant mathematical equation. → mathematical elegance.

→ Euler; → formula.

1) (n.) General: The shape and structure of something as distinguished from its material.
Philosophy: The structure, pattern, organization, or essential nature of anything. Structure or pattern as distinguished from matter.
Logic: The abstract relations of terms in a proposition, and of propositions to one another.
2) (v.intr.) of form.
3) (v.tr.) of form.

From O.Fr. forme, from L. forma "form, mold, shape, case," origin unknown.

1) Dis, disé "form, appearance," variants -diz, -diš (tandis "body form, like a body; effigy;" mâhdis "moon-like;" šabdiz "night color; a horse of dark rusty color;" andiš- "to think, contemplate"), from Mid.Pers. dêsag "form, appearance," dêsidan "to form, build;" Av. daēs- "to show," daēsa- "sign, omen;" cf. Skt. deś- "to show, point out;" PIE *deik- "to show" (cf. Gk. deiknumi "to show," dike "manner, custom;" L. dicere "to utter, say;" O.H.G. zeigon, Ger. zeigen "to show;" O.E. teon "to accuse," tæcan "to teach").
2) and 3) corresponding infintives of dis, as above.

1) According to, or following established or prescribed forms, conventions, etc.
2) Math., logic: Of a proof, in strict logical form with a justification for every step.
3) Math., logic: Of a calculation, correct in form; made with strict justification for every step; of or pertaining to manipulation of symbols without regard to their meaning.
4) → formal language.
5) → formal logic.

M.E. formal, formel, from L. formalis, from → form + → -al.

Diseyi, desevar, from dis, → form, + adj. suffixes -i and -var.

A language designed for use in situations in which natural language is unsuitable, as for example in → mathematics, → logic, or → computer  → programming. The symbols and formulas of such languages stand in precisely specified syntactic and semantic relations to one another (Dictionary.com).

→ formal; → language.

The traditional or → classical logic in which the → validity or → invalidity of a conclusion is deduced from two or more statements (→ premises). Based on Aristotle's (384-322 BC) theory of → syllogism, systematized in his book "Organon," its focus is not on what is stated (the content) but on the structure (form) of the → argument and the validity of the inference drawn from the premises of the argument; if the premises are true then the logical consequence must also be true. Formal logic is → bivalent, that is it recognizes only two → truth values: → true and → false. The basic principles of formal logic are: 1) → principle of identity, 2) → principle of excluded middle, and 3) → principle of non-contradiction. See also → symbolic logic, → fuzzy logic.

→ formal; → logic.

In logic and mathematics, a system in which statements can be constructed and manipulated with logical rules.

→ formal; → system.