radiann.

Brit.

/ˈreɪdɪən/, U.S.

/ˈreɪdiən/

Origin: Formed within English, by derivation. Etymons: radius n., radial adj., -an suffix.

Etymology: < either radius n. or radial adj. + -an suffix.Two separate individuals seem to have arrived at the term independently: Sir Thomas Muir (1844–1934), mathematician and educationist, and James Thomson (1822–92), mechanical engineer; compare the following:1910 T. Muir in Nature 7 Apr. 156 I wrote to him [sc. Alexander J. Ellis, in 1874], and he agreed at once for the form ‘radian’, on the ground that it could be viewed as a contraction for ‘radial angle’.1910 J. Thomson in Nature 16 June 460/1 I shall be very pleased to send Dr. Muir a copy of my father's examination questions of June, 1873, containing the word ‘radian’; and when Dr. Muir returns to England I should like to show him my father's copy of the ‘Imperial Dictionary’ containing a note in his own hand saying that he had proposed the word in July, 1871... It thus appears that ‘radian’ was thought of independently by Dr. Muir and my father, and, what is really more important than the exact form of the name, they both independently thought of the necessity of giving a name to the unit-angle. With the reference to Alexander John Ellis (1814–90), phonetician and mathematician, in quot. 1910¹ compare the following:1874 A. J. Ellis Algebra identified with Geom. 82/1 2 π radial angles = 4 right angles.

Geometry.

A unit of angle (now incorporated in the International System of Units), defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. Symbol rad.2π radians are equivalent to 360 degrees, and one radian is approx. 57.2958 degrees.

ΘΚΠ

the world > relative properties > number > geometry > angle > [noun] > degree > other measurements of angles

grade1801

radian1874

steradian1881

rad1913

grad1959

sr-

1874 Jrnl. Soc. Telegr. Engineers 3 222 (note) ‘Radian’ is a most valuable word, introduced by Professor James Thomson to denote the angle whose arc is equal to radius. It is the hitherto nameless ‘unit angle’ of the Cambridge and other mathematical books.

1881 G. B. Halsted Mensuration 24 The number which expresses any angle in radians also expresses its intercepted arc in terms of the radius.

1936 R. S. Glasgow Princ. Radio Engin. i. 1 If a coil of N turns is rotated with a constant angular velocity of ω radians per second in a uniform magnetic field, the electromagnetic force (e.m.f.) induced in it at any instant will be [etc.].

1959 F. J. Camm Gears (‘Pract. Engin.’ Pocket Bk. No. 5) 12 This involute function of θ is denoted by inv. θ and is equal to tan θ − θ, where θ is measured in radians.

2016 M. Beech Wayward Comet iii. 117 The required solution is E = 1.359085 radians (corresponding to 77.87 degrees).

This entry has been updated (OED Third Edition, June 2008; most recently modified version published online June 2022).

单词	radian
释义	radiann. Brit. /ˈreɪdɪən/, U.S. /ˈreɪdiən/ Origin: Formed within English, by derivation. Etymons: radius n., radial adj., -an suffix. Etymology: < either radius n. or radial adj. + -an suffix.Two separate individuals seem to have arrived at the term independently: Sir Thomas Muir (1844–1934), mathematician and educationist, and James Thomson (1822–92), mechanical engineer; compare the following:1910 T. Muir in Nature 7 Apr. 156 I wrote to him [sc. Alexander J. Ellis, in 1874], and he agreed at once for the form ‘radian’, on the ground that it could be viewed as a contraction for ‘radial angle’.1910 J. Thomson in Nature 16 June 460/1 I shall be very pleased to send Dr. Muir a copy of my father's examination questions of June, 1873, containing the word ‘radian’; and when Dr. Muir returns to England I should like to show him my father's copy of the ‘Imperial Dictionary’ containing a note in his own hand saying that he had proposed the word in July, 1871... It thus appears that ‘radian’ was thought of independently by Dr. Muir and my father, and, what is really more important than the exact form of the name, they both independently thought of the necessity of giving a name to the unit-angle. With the reference to Alexander John Ellis (1814–90), phonetician and mathematician, in quot. 1910¹ compare the following:1874 A. J. Ellis Algebra identified with Geom. 82/1 2 π radial angles = 4 right angles. Geometry. A unit of angle (now incorporated in the International System of Units), defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. Symbol rad.2π radians are equivalent to 360 degrees, and one radian is approx. 57.2958 degrees. ΘΚΠ the world > relative properties > number > geometry > angle > [noun] > degree > other measurements of angles grade1801 radian1874 steradian1881 rad1913 grad1959 sr- 1874 Jrnl. Soc. Telegr. Engineers 3 222 (note) ‘Radian’ is a most valuable word, introduced by Professor James Thomson to denote the angle whose arc is equal to radius. It is the hitherto nameless ‘unit angle’ of the Cambridge and other mathematical books. 1881 G. B. Halsted Mensuration 24 The number which expresses any angle in radians also expresses its intercepted arc in terms of the radius. 1936 R. S. Glasgow Princ. Radio Engin. i. 1 If a coil of N turns is rotated with a constant angular velocity of ω radians per second in a uniform magnetic field, the electromagnetic force (e.m.f.) induced in it at any instant will be [etc.]. 1959 F. J. Camm Gears (‘Pract. Engin.’ Pocket Bk. No. 5) 12 This involute function of θ is denoted by inv. θ and is equal to tan θ − θ, where θ is measured in radians. 2016 M. Beech Wayward Comet iii. 117 The required solution is E = 1.359085 radians (corresponding to 77.87 degrees). This entry has been updated (OED Third Edition, June 2008; most recently modified version published online June 2022). < n.1874
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