Eulern.

Brit.

/ˈɔɪlə/,

/ˈjuːlə/, U.S.

/ˈɔɪlər/

Etymology: < the name of Leonard Euler (see Eulerian adj.).

1. Used attributively, in combinations, or in the possessive to designate principles, effects, etc., discovered by Euler or arising out of his work.

ΚΠ

1847 London, Edinb. & Dublin Philos. Mag. 3rd Ser. 30 424 Recent researches.., in reference to the new analytical theory of imaginary quantities, have revived attention to Euler's theorem, that the sum of four squares multiplied by the sum of four squares produces the sum of four squares.

1889 Cent. Dict. Euler's numbers, the numbers E₂, E₄, etc., which occur in the development of sec x by Maclaurin's theorem: namely, sec x = 1 + E₂x²/2! + E₄x⁴/4! + etc.

1889 Cent. Dict. Euler's solution, a solution of a biquadratic after the second term has been got rid of.

1940 Jrnl. Royal Aeronaut. Soc. 44 43 The term quasi-Euler is used to distinguish the failure which occurs by buckling over the greatest wave length which the supports allow from the corrugated failure fixed by the minimum condition. Although the skin fails in an Euler curve it is not a true Euler effect.

1947 R. Courant & H. E. Robbins What is Math.? (ed. 4) v. 240 On the basis of Euler's formula it is easy to show that there are no more than five regular polyhedra.

1961 New Scientist 16 Mar. 698/3 The result V + F − E = 2 was originally derived for polyhedra: this is the Euler-Descartes relation, known to Descartes but first explicitly proved by Euler.

2. Euler's constant n. Mathematics the constant that is the limit of the sum 1 + ¹/ ₂ + … + ¹/ _n − log n as n tends to infinity, approximately equal to 0.577215665 (it is not yet known whether this number is rational or irrational).

ΚΠ

1881 Encycl. Brit. XIII. 49/1 This limit, whose importance was first noticed by Euler (Acta Petropolis, 1734), is now usually called Euler's Constant.

1953 W. Rudin Princ. Math. Anal. viii. 163 1 + ½ +…+ (1/n)−log n..converges. (The limit, often denoted by γ, is called Euler's constant. Its value is 0·5772...).

1990 Nucleic Acids Res. 18 317/2 We estimated the parameters λ and u, which describe the distribution of maximal scores for a given probe, by λ = π/√6V and u = μ − γ/λ where γ is Euler's constant (0.577...), μ is the sample mean, and V is the sample variance.

This entry has not yet been fully updated (first published 1972; most recently modified version published online March 2022).

单词	euler
释义	Eulern. Brit. /ˈɔɪlə/, /ˈjuːlə/, U.S. /ˈɔɪlər/ Etymology: < the name of Leonard Euler (see Eulerian adj.). 1. Used attributively, in combinations, or in the possessive to designate principles, effects, etc., discovered by Euler or arising out of his work. ΚΠ 1847 London, Edinb. & Dublin Philos. Mag. 3rd Ser. 30 424 Recent researches.., in reference to the new analytical theory of imaginary quantities, have revived attention to Euler's theorem, that the sum of four squares multiplied by the sum of four squares produces the sum of four squares. 1889 Cent. Dict. Euler's numbers, the numbers E₂, E₄, etc., which occur in the development of sec x by Maclaurin's theorem: namely, sec x = 1 + E₂x²/2! + E₄x⁴/4! + etc. 1889 Cent. Dict. Euler's solution, a solution of a biquadratic after the second term has been got rid of. 1940 Jrnl. Royal Aeronaut. Soc. 44 43 The term quasi-Euler is used to distinguish the failure which occurs by buckling over the greatest wave length which the supports allow from the corrugated failure fixed by the minimum condition. Although the skin fails in an Euler curve it is not a true Euler effect. 1947 R. Courant & H. E. Robbins What is Math.? (ed. 4) v. 240 On the basis of Euler's formula it is easy to show that there are no more than five regular polyhedra. 1961 New Scientist 16 Mar. 698/3 The result V + F − E = 2 was originally derived for polyhedra: this is the Euler-Descartes relation, known to Descartes but first explicitly proved by Euler. 2. Euler's constant n. Mathematics the constant that is the limit of the sum 1 + ¹/ ₂ + … + ¹/ _n − log n as n tends to infinity, approximately equal to 0.577215665 (it is not yet known whether this number is rational or irrational). ΚΠ 1881 Encycl. Brit. XIII. 49/1 This limit, whose importance was first noticed by Euler (Acta Petropolis, 1734), is now usually called Euler's Constant. 1953 W. Rudin Princ. Math. Anal. viii. 163 1 + ½ +…+ (1/n)−log n..converges. (The limit, often denoted by γ, is called Euler's constant. Its value is 0·5772...). 1990 Nucleic Acids Res. 18 317/2 We estimated the parameters λ and u, which describe the distribution of maximal scores for a given probe, by λ = π/√6V and u = μ − γ/λ where γ is Euler's constant (0.577...), μ is the sample mean, and V is the sample variance. This entry has not yet been fully updated (first published 1972; most recently modified version published online March 2022). < n.1847
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