Pellianadj.n.

Brit.

/ˈpɛlɪən/, U.S.

/ˈpɛliən/

Origin: From a proper name, combined with an English element; modelled on a Latin lexical item. Etymons: proper name Pell , -ian suffix.

Etymology: < the name of John Pell, English mathematician (1610–85) + -ian suffix, after post-classical Latin Pellianus (1767: see below).Although the importance of the equation was first recognized by Fermat, and the method for its solution was found by W. Brouncker (1657–8), it was, by some misunderstanding, named after Pell by L. Euler:1767 L. Euler in Novi Commentarii Acad. Sci. Imp. Petropolitanæ 11 28 (heading) De usu novi algorithmi in problemate Pelliano solvendo.1767 L. Euler in Novi Commentarii Acad. Sci. Imp. Petropolitanæ 11 31 pp = lqq + 1... Atque hoc est illud problema olim quidem maxime celebratum a solutionis ingeniosissimae auctore Pellianum vocatum.

Mathematics.

Designating a Pell equation. Also as n.: a Pell equation. Cf. Pell n.³

ΘΚΠ

the world > relative properties > number > algebra > [adjective] > relating to expressions > relating to equations

algebraic1657

lateral1670

explicable1706

unreduced1762

homogeneous1815

resolvent1860

Pellian1862

equational1864

canonizant1879

variational1879

unilateral1884

non-dimensional1904

open1937

inhomogeneous1943

stiff1952

1862 Rep. Brit. Assoc. Advancem. Sci. 1861 i. 314 There does not seem to be any ground for attributing either the problem or its solution to Pell... Nevertheless the equation T² − DU² = 1 is often called the Pellian equation after him, probably upon Euler's authority.

1875 A. Cayley Coll. Math. Papers IX. 477 The Pellian equation is y² = ax² + 1, a being a given integer number, which is not a square (or rather, if it be, the only solution is y = 1, x = 0), and x, y being numbers to be determined: what is required is the least values of x, y, since these, being known, all other values can be found.

1952 Amer. Math. Monthly 59 575 (title) A generalization of the Pellian equation and applications.

1974 Sci. Amer. July 118/3 The Pellian for square hexes is 3x² + 1 = y², which is solved by finding the convergents of the continued fraction for the square root of 3.

1995 Acta Arithmetica 71 260 This is a system of two Pellian equations, each having exactly four classes of solutions.

This entry has been updated (OED Third Edition, September 2005; most recently modified version published online March 2022).

单词	pellian
释义	Pellianadj.n. Brit. /ˈpɛlɪən/, U.S. /ˈpɛliən/ Origin: From a proper name, combined with an English element; modelled on a Latin lexical item. Etymons: proper name Pell , -ian suffix. Etymology: < the name of John Pell, English mathematician (1610–85) + -ian suffix, after post-classical Latin Pellianus (1767: see below).Although the importance of the equation was first recognized by Fermat, and the method for its solution was found by W. Brouncker (1657–8), it was, by some misunderstanding, named after Pell by L. Euler:1767 L. Euler in Novi Commentarii Acad. Sci. Imp. Petropolitanæ 11 28 (heading) De usu novi algorithmi in problemate Pelliano solvendo.1767 L. Euler in Novi Commentarii Acad. Sci. Imp. Petropolitanæ 11 31 pp = lqq + 1... Atque hoc est illud problema olim quidem maxime celebratum a solutionis ingeniosissimae auctore Pellianum vocatum. Mathematics. Designating a Pell equation. Also as n.: a Pell equation. Cf. Pell n.³ ΘΚΠ the world > relative properties > number > algebra > [adjective] > relating to expressions > relating to equations algebraic1657 lateral1670 explicable1706 unreduced1762 homogeneous1815 resolvent1860 Pellian1862 equational1864 canonizant1879 variational1879 unilateral1884 non-dimensional1904 open1937 inhomogeneous1943 stiff1952 1862 Rep. Brit. Assoc. Advancem. Sci. 1861 i. 314 There does not seem to be any ground for attributing either the problem or its solution to Pell... Nevertheless the equation T² − DU² = 1 is often called the Pellian equation after him, probably upon Euler's authority. 1875 A. Cayley Coll. Math. Papers IX. 477 The Pellian equation is y² = ax² + 1, a being a given integer number, which is not a square (or rather, if it be, the only solution is y = 1, x = 0), and x, y being numbers to be determined: what is required is the least values of x, y, since these, being known, all other values can be found. 1952 Amer. Math. Monthly 59 575 (title) A generalization of the Pellian equation and applications. 1974 Sci. Amer. July 118/3 The Pellian for square hexes is 3x² + 1 = y², which is solved by finding the convergents of the continued fraction for the square root of 3. 1995 Acta Arithmetica 71 260 This is a system of two Pellian equations, each having exactly four classes of solutions. This entry has been updated (OED Third Edition, September 2005; most recently modified version published online March 2022). < adj.n.1862
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