sheaf
Language: English
Part of speech: noun
Pronunciation: enpr: shēf
ipa: /ʃiːf/
rhymes: -iːf
Forms: form: sheaves
form: sheafs
Etymology: From Middle English scheef, from Old English sċēaf, from Proto-West Germanic *skaub, from Proto-Germanic *skauba- (“sheaf”).
Cognates
Akin to West Frisian skeaf (“sheaf”), Dutch schoof (“sheaf”), German Schaub, Old Norse skauf (“a fox's tail”). Compare further Gothic 𐍃𐌺𐌿𐍆𐍄 (skuft, “hair of the head”), German Schopf (“tuft”).
Senses: examples: text: O, let me teach you how to knit again / This scattered corn into one mutual sheaf, / These broken limbs again into one body.
ref: c. 1588–1593 (date written), William Shakespeare, “The Lamentable Tragedy of Titus Andronicus”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, →OCLC, [Act V, scene iii], line 70:
text: Ev’n while the Reaper fills his greedy hands, / And binds the golden Sheafs in brittle bands
ref: 1697, Virgil, “The First Book of the Georgics”, in John Dryden, transl., The Works of Virgil: Containing His Pastorals, Georgics, and Æneis. […], London: […] Jacob Tonson, […], →OCLC, page 60, lines 429–430:
synonyms: reap
glosses: A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.
examples: text: a sheaf of paper
text: Together the two men march up the aisle and mount the dais, and while Muspole shakes hands with the chairman and his lady, the major draws a sheaf of notes from a briefcase and lays them on the table.
ref: 1986, John le Carré, A Perfect Spy:
synonyms: bundle
glosses: Any collection of things bound together.
examples: text: The sheaf of arrows shook, and rattled in the case.
ref: 1700, John Dryden, Palamon and Arcite:
glosses: A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.
examples: text: Arrows were anciently made of reeds, afterwards of cornel wood, and occasionally of every species of wood: but according to Roger Ascham, ash was best; arrows were reckoned by sheaves, a sheaf consisted of twenty-four arrows.
ref: 1786, Francis Grose, A Treatise on Ancient Armour and Weapons, page 34:
glosses: A quantity of arrows, usually twenty-four.
topics: engineering
mechanical
mechanical-engineering
natural-sciences
physical-sciences
glosses: A sheave.
topics: mathematics
sciences
glosses: An abstract construct in topology that associates data to the open sets of a topological space (i.e. a presheaf) in such a way so as to make the local and global data compatible, generalizing the situation of functions, fiber bundles, manifold structure, etc. on a topological space. Formally, a presheaf ℱ whose sections are, in a technical sense, uniquely determined by their restrictions onto smaller sets: that is, given an open cover U_i of U:
If two sections over U agree under restriction to every U_i, then the sections are the same.
topics: mathematics
sciences
glosses: An abstract construct in topology that associates data to the open sets of a topological space (i.e. a presheaf) in such a way so as to make the local and global data compatible, generalizing the situation of functions, fiber bundles, manifold structure, etc. on a topological space. Formally, a presheaf ℱ whose sections are, in a technical sense, uniquely determined by their restrictions onto smaller sets: that is, given an open cover U_i of U:
Given a family of sections s_i∈ℱ(U_i) such that all pairs (s_i,s_j) agree under restriction to U_i∩U_j, there is a (unique) section s over U whose restriction to U_i is s_i.
Derived terms: B-sheaf
indsheaf
sheaf theory
sheafwise
structure sheaf