curvature

Etymology

It is borrowed from Latin curvātūra (“curved shape, bend”),^[2][3][4] from curvātus, the past participle of curvō (“to bend”), and the suffix -ūra.^[2][4][5] The verb is from curvus (“crooked, curved, bent”),^[4][3] from Proto-Indo-European *sker- (“to turn, bend”).^[3][4] The Shorter Oxford and the Oxford Dictionary of English take the word through Old French,^[6][7] while the OED treats it as a direct borrowing from Latin and compares curvature, recorded before 1544, and courbure.^[2] It is related to curve.^[3][7]

Earliest recorded meaning

A curved part of something, a curve: perhaps before 1425, in a translation of Guy de Chauliac's Grande Chirurgie.^[2] Dictionary.com dates the word to late Middle English,^[8] while Merriam-Webster gives 1603 and Etymonline the 1660s.^[5][3]

Semantic evolution

The abstract sense, the action of curving or the state of being curved, is recorded from before 1460, in Knyghthode and Bataile;^[2] Etymonline defines its 17th-century use as continuous bending, the essential character of a curve.^[3] Johnson (1755) glossed it as crookedness, inflexion, or manner of bending.^[9] Medicine used it from 1762 for an abnormal curve of the spine.^[2] Mathematics made it a measured quantity: the amount by which a curve departs from a straight line, from 1710 in Harris's Lexicon Technicum,^[2] with the radius of curvature from 1712.^[2] In non-Euclidean geometry it was applied to space itself from 1873.^[3][2] A verb curvature, to curve, is recorded once, before 1811.^[2]

Timeline

• c. 1425 – a curved part of something, a curve.^[2]
• before 1460 – the action of curving; the state of being curved.^[2]
• 1710 – in geometry, the degree to which a curve deviates from a straight line.^[2]
• 1712 – radius of curvature.^[2]
• 1762 – an abnormal curve of the spine.^[2]
• 1873 – the curvature of space, in non-Euclidean geometry.^[2][3]

Meanings

Noun

1. The act of curving, or the state or degree of being curved.^[5][2][10]
2. A curved part of something; a bend.^[5][10][2]
3. (medicine) An abnormal curving of a part of the body, as in curvature of the spine.^[10][2]
4. (geometry) The rate at which a curve departs from a straight line, or a surface from a plane, measured by the turning of the tangent along the arc; for a circle, the reciprocal of its radius.^[10][5][2]
5. (geometry) The degree to which a space or manifold differs from Euclidean space.^[2]

Word family

• center of curvature
• radius of curvature

Related words

• curve
• curvilinear
• curvaceous

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h i j k l m n o p q r s t u Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b c d e f g h Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
4. ^ a b c d The American Heritage Dictionary of the English Language (online 2024), 5th ed., Boston: Houghton Mifflin Harcourt
5. ^ a b c d e Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
6. ^ Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
7. ^ a b Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
8. ^ Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
9. ^ Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.
10. ^ a b c d Collins English Dictionary (2023), Glasgow: HarperCollins