English
sheaf
Pronunciation
Noun

sheaf (plural sheaves)

1. A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.
• 1593, William Shakespeare, Titus Andronicus, Act V, Scene III, line 70:
O, let me teach you how to knit again / This scattered corn into one mutual sheaf, / These broken limbs again into one body.
• circa 1697 John Dryden, “Georgic I”, in The Works of Virgil:
E’en while the reaper fills his greedy hands, / And binds the golden sheaves in brittle bands
2. Any collection of things bound together; a bundle.
a sheaf of paper
3. A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.
4. A quantity of arrows, usually twenty-four.
• 1786, Francis Grose, A Treatise on Ancient Armour and Weapons, page 34:
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.
5. (mechanical) A sheave.
6. (mathematics) An abstract construct in topology that associates data to the open sets of a topological space, together with well-defined restrictions from larger to smaller open sets, subject to the condition that compatible data on overlapping open sets corresponds, via the restrictions, to a unique datum on the union of the open sets.
• , "[[w:Differentiable manifold#Structure sheaf", Wikipedia
Sometimes, it can be useful to use an alternative approach to endow a manifold with a Ck-structure. Here k = 1, 2, ..., ∞, or ω for real analytic manifolds. Instead of considering coordinate charts, it is possible to start with functions defined on the manifold itself. The structure sheaf of M, denoted Ck, is a sort of functor that defines, for each open set U ⊂ M, an algebra Ck(U) of continuous functions U → R.
Synonyms
• (bundle of grain) reap
Translations
Translations
Translations
Verb

sheaf (sheafs, present participle sheafing; past and past participle sheafed)

1. (transitive) To gather and bind into a sheaf; to make into sheaves
to sheaf wheat
2. (intransitive) To collect and bind cut grain, or the like; to make sheaves.
• 1599, William Shakespeare, As You Like It, Act III, Scene II, line 107:
They that reap must sheaf and bind; Then to cart with Rosalind.

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