sheaf

From Middle English scheef, from Old English sċēaf, from Proto-West Germanic *skaub, from Proto-Germanic *skauba- (“sheaf”).

• enPR: shēf, IPA^(key): /ʃiːf/

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• Rhymes: -iːf

Sheaves

sheaf (plural sheaves or sheafs)

1. A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.

   Synonym: reap

   • 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:

     O, let me teach you how to knit again / This scattered corn into one mutual sheaf, / These broken limbs again into one body.

   • 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:

     Ev’n while the Reaper fills his greedy hands, / And binds the golden Sheafs in brittle bands

2. Any collection of things bound together.

   Synonym: bundle

   a sheaf of paper

   • 1986, John le Carré, A Perfect Spy:

     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.

3. A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.
   • 1700, John Dryden, Palamon and Arcite:

     The sheaf of arrows shook, and rattled in the case.

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 (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 ${\displaystyle {\mathcal {F}}}$ whose sections are, in a technical sense, uniquely determined by their restrictions onto smaller sets: that is, given an open cover ${\displaystyle \{U_{i}\}}$ of ${\displaystyle U}$:
   1. If two sections over ${\displaystyle U}$ agree under restriction to every ${\displaystyle U_{i}}$, then the sections are the same.
   2. Given a family of sections ${\displaystyle s_{i}\in {\mathcal {F}}(U_{i})}$ such that all pairs ${\displaystyle (s_{i},s_{j})}$ agree under restriction to ${\displaystyle U_{i}\cap U_{j}}$, there is a (unique) section ${\displaystyle s}$ over ${\displaystyle U}$ whose restriction to ${\displaystyle U_{i}}$ is ${\displaystyle s_{i}}$.

• indsheaf
• sheafwise

sheaf (third-person singular simple present sheafs, present participle sheafing, simple 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.
   • c. 1598–1600 (date written), William Shakespeare, “As You Like It”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, →OCLC, [Act III, scene ii], line 107:

     They that reap must sheaf and bind; Then to cart with Rosalind.

• SHAEF, Shefa