An Etymological Dictionary of Astronomy and Astrophysics
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In particle physics, a quantum number attributed to elementary particles which is conserved in nuclear reactions. It is +1 for a lepton, -1 for an antilepton and 0 for other particles.

→ lepton; → number.

The number of molecules in 1 cm³ of an ideal gas (2.687 x 10¹⁹ per cm³).

Joseph Loschmidt (1821-1895), Austrian physicist.

The ratio of the speed of a moving object to the → sound speed in the medium through which the object is traveling.

Named after the Austrian physicist Ernst Mach (1838-1916); → number.

A → dimensionless quantity used in → magnetohydrodynamics to describe the relative balance of → kinematic viscosity to → magnetic diffusion. It is described by: P_r = σμ₀ν = ν/η, where σ is the → conductivity of the fluid, μ₀ is the → magnetic permeability of the fluid, ν is the kinematic viscosity of the fluid, and η is the → magnetic diffusivity.

→ magnetic; → Prandtl number.

In atomic physics, a quantum number that denotes the energy levels available within a subshell. Designated by the letter m, it is one of a set of quantum numbers which describe the unique quantum state of an electron.

→ magnetic; → quantum; → number.

A → dimensionless quantity used in → magnetohydrodynamics to describe the relative balance of → magnetic advection to → magnetic diffusion. It is given by: R_m = σμ₀νLU₀, where σ is the → conductivity of the fluid, μ₀ is the → magnetic permeability of the fluid, L is he characteristic length scale of the fluid flow, and U₀ the characteristic velocity of the flow. A typical value for the Earth is R_m ~ 200.

→ magnetic; → Reynolds number.

The total number of → protons and → neutrons in the → atomic nucleus (symbol A). The mass number is written either after the → chemical element name or as a superscript to the left of an element's symbol. For example, the most common isotope of oxygen is oxygen-16, or ¹⁶O, which has 8 protons and 8 neutrons.

→ mass; → number.

Either a member of the set of positive integers 1, 2, 3, ..., or the set of non-negative integers 0, 1, 2, 3, ... There seems to be no general agreement about whether to include 0 in the set of natural numbers.

→ natural; → number.

A → real number that is less than zero. A negative number is indicated by the → minus sign.

→ negative; → number.

1) Any real or complex numeral quantity.
2) The sum, total, count, or aggregate of a collection of units.

From M.E. nombre, from O.Fr. nombre, from L. numerus "a number, quantity," from PIE base *nem- "to divide, distribute, allot."

Adad, loan from Ar.
Šomâr, šomâré, noun from šomârdan "to count, reckon, calculate, enumerate, account for," from Mid.Pers. ôšmârtan; Av. base (š)mar- "to have in mind, remember, recall," pati-šmar- "to recall; to long for," hišmar-; cf. Skt. smar- "to remember, become aware," smarati "he remembers;" L. memor, memoria; Gk. mermera "care," merimna "anxious thought, sorrow," martyr "witness."

Number of a particular type of object found in each unit volume.

→ number; → density.

The → base of the → natural logarithm. It is defined as: e = lim (1 + 1/n)ⁿ when n→ ∞. For n = 1, e = 2 and for n = 10, e = 2.5937424601, etc. The number e is → irrational (Euler, 1737) and → transcendental (Hermite, 1873).

→ number;

Symbol, π, for the ratio of the circumference of a circle to its diameter in Euclidean geometry; a fundamental mathematical constant, equal to 3.14159... π is an → irrational number (Lambert, 1761) and also a → transcendental number (von Lindemann, 1882). The most accurate determination of π prior to the Scientific Revolution belongs to the Iranian mathematician Jamshid Kashani, who gave 16 correct decimal places in A.D. 1424. With the advent of → calculus and more recently the invention of powerful computers, the decimal representation of π has now been computed to more than 10¹² digits.

The π notation, representing the first letter of the Gk. word περιμετρον → perimeter, was first used by the British mathematician William Jones (1675-1749) in 1706. Its use was generalized after its adoption by the Swiss mathematician Leonard Euler (1707-1783) in 1737; → number.

Same as → numeral system.

→ number; → system.

The conversion of a → number system with a given → base to another system with a different base; such as the conversion of a → decimal number (base 10) to a → binary number system (base 2). In order to convert a number into its representation in a different number base, we have to express the number in terms of powers of the other base. For example, to convert the decimal number 100 to base 3, we must figure out how to express 100 as the sum of powers of 3. We proceed as follows:
1: Divide the decimal number to be converted (100) by the value of the new base (3).
2: Get the remainder from Step 1 (that is 1) as the rightmost digit (least significant digit) of new base number.
3: Divide the quotient of the previous divide (33) by the new base.
4: Record the remainder from Step 3 (0) as the next digit (to the left) of the new base number.
Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step 3 (2 and 0).
The last remainder thus obtained (1) will be the most significant digit of the new base number.
Therefore, 100₁₀ = 10201₃.
Conversely, to convert from another base to decimal we must:
1: Determine the column (positional) value of each digit.
2: Multiply the obtained column values (in Step 1) by the digits in the corresponding columns.
3: Sum the products calculated in Step 2. The total is the equivalent value in decimal.
For example, the binary number 1100100 is determined by computing the place value of each of the digits of the number:
(1 × 2⁶) + (1 × 2⁵) + (0 × 2⁴) + (0 × 2³) + (1 × 2²) + (0 × 2¹) + (0 × 2⁰) = 64 + 32 + 0 + 0 + 4 + 0 + 0 = 100.

→ number; → system; → conversion.

The branch of mathematics that studies the relationship between integers and their generalization.

→ number; → theory.

1) A number which defines the position or rank of something in a series, in contrast to → cardinal number. For example, first, second, tenth, etc.
2) In → set theory, the order type of a → well-ordered set. Also called ordinal.

→ ordinal; → number.

The total number of electrons that an atom either gains or loses in order to form a chemical bond with another atom. In other words, the charge that atom would have if the compound was composed of ions. The oxidation number of an atom is zero in a neutral substance that contains atoms of only one element. Same as → oxidation state.

→ oxidation; → number.

An → integer that is equal to the → sum of its → positive  → divisors, not including itself. For example 6, because its positive divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. Two other examples are 28 and 496.

→ perfect; → number.

Symbol, π, for the ratio of the circumference of a circle to its diameter in Euclidean geometry; a fundamental mathematical constant, equal to 3.14159... π is an → irrational number (Lambert, 1761) and also a → transcendental number (von Lindemann, 1882). The most accurate determination of π prior to the Scientific Revolution belongs to the Iranian mathematician Jamshid Kashani, who gave 16 correct decimal places in A.D. 1424. With the advent of → calculus and more recently the invention of powerful computers, the decimal representation of π has now been computed to more than 10¹² digits.

The π notation, representing the first letter of the Gk. word περιμετρον → perimeter, was first used by the British mathematician William Jones (1675-1749) in 1706. Its use was generalized after its adoption by the Swiss mathematician Leonard Euler (1707-1783) in 1737; → number.