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

A number which taken three times as a factor produces another number, the cube of the given factor.

→ cube; → root.

A → root x₀ of function f(x), if f(x₀) = 0, df/dx | x₀ = 0, and d²f/dx² | x₀≠ 0. See also → simple root.

→ double; → root.

1) Math.: A quantity that, when multiplied by itself a certain number of times, produces a given quantity. For example, since 3 × 3 × 3 × 3 = 81, 3 is a fourth root of 81.
2) Math.: A solution to an equation f(x) = 0. We say that x₀ is a root or zero of a → polynomial if f(x₀) = 0. For example, the roots of the equation x² - 9 = 0 are +3 and -3.
3) In → graph theory, a special → vertex that turns a → tree into a → rooted tree or a graph into a → rooted graph.

From M.E., from O.E. rot, from O.N. rot "root;" cf. O.H.G. wurz "plant, herb;" Ger. Wurz; cognate with L. radix, radius "staff;" Gk. rhiza "root;" Albanian rrânzë "root;" PIE base *u(e)rad- "twig, root."

Rišé "root" (dialectal Tabari rexa; Kurd. regez, riše), from Mid.Pers. rêšak "root," maybe ultimately related to PIE *u(e)rad-, as above, although the Skt. offshoot is absent.

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.

In → graph theory, a → graph that has one of its → vertices, called the → root, distinguished from the others.

→ root; → graph.

In → graph theory, a → tree in which one → vertex is distinguished from the other vertices and is called the root.

→ root; → tree.

A → rootx₀ of function f(x), if f(x₀) = 0 and df/dx | x₀ = 0. See also → double root.

→ simple; → root.

Quantity which when multiplied by itself produces another quantity.

→ square; → root.