Etymology
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wrinkle (v.)
early 15c. (transitive), probably from stem of Old English gewrinclod "wrinkled, crooked, winding," past participle of gewrinclian "to wind, crease," from perfective prefix ge- + -wrinclian "to wind," from Proto-Germanic *wrankjan, from a nasalized variant of *werg- "to turn," from PIE root *wer- (2) "to turn, bend." Intransitive sense from 1610s. Related: Wrinkled; wrinkling.
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wrinkle (n.)
"fold or crease in the extenal body," late 14c.; in cloth or clothing from early 15c., probably from wrinkle (v.). Meaning "defect, problem" first recorded 1640s; that of "idea, device, notion" (especially a new one) is from 1817.
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wrinkly (adj.)
early 15c. (in reference to the penis), from wrinkle (n.) + -y (2). As teen slang noun for "old person," from 1972 ("old" being relative; a British reference from 1982 applies it to people in their 40s).
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*wer- (2)

Proto-Indo-European root forming words meaning "to turn, bend."

It forms all or part of: adverse; anniversary; avert; awry; controversy; converge; converse (adj.) "exact opposite;" convert; diverge; divert; evert; extroversion; extrovert; gaiter; introrse; introvert; invert; inward; malversation; obverse; peevish; pervert; prose; raphe; reverberate; revert; rhabdomancy; rhapsody; rhombus; ribald; sinistrorse; stalwart; subvert; tergiversate; transverse; universe; verbena; verge (v.1) "tend, incline;" vermeil; vermicelli; vermicular; vermiform; vermin; versatile; verse (n.) "poetry;" version; verst; versus; vertebra; vertex; vertigo; vervain; vortex; -ward; warp; weird; worm; worry; worth (adj.) "significant, valuable, of value;" worth (v.) "to come to be;" wrangle; wrap; wrath; wreath; wrench; wrest; wrestle; wriggle; wring; wrinkle; wrist; writhe; wrong; wroth; wry.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit vartate "turns round, rolls;" Avestan varet- "to turn;" Hittite hurki- "wheel;" Greek rhatane "stirrer, ladle;" Latin vertere (frequentative versare) "to turn, turn back, be turned; convert, transform, translate; be changed," versus "turned toward or against;" Old Church Slavonic vrŭteti "to turn, roll," Russian vreteno "spindle, distaff;" Lithuanian verčiu, versti "to turn;" German werden, Old English weorðan "to become;" Old English -weard "toward," originally "turned toward," weorthan "to befall," wyrd "fate, destiny," literally "what befalls one;" Welsh gwerthyd "spindle, distaff;" Old Irish frith "against."

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rumple (v.)

"to wrinkle, make uneven," c. 1600, in rumpled, of uncertain origin, perhaps a variant of rimple "to wrinkle" (c. 1400), from Old English hrympel "wrinkle" (possibly influenced by Middle Dutch rumpelen), related to Old English hrimpan "to fold, wrinkle" (see ramp (v.)). Related: Rumpled; rumpling. As a noun from c. 1500, "a wrinkle, a fold."

Also compare Middle English runkle "become wrinkled" (late 14c.), runkel (n.) "a wrinkle" (early 14c.), probably from Old Norse hrukka.

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corrugate (v.)

"to wrinkle, to draw or contract into folds," 1610s, from Latin corrugatus, past participle of corrugare "to make full of wrinkles, wrinkle very much" (also "produce loathing, cause disgust"), from assimilated form of com-, here perhaps an intensive prefix (see com-), + rugare "to wrinkle," from ruga "crease, groove," which is of uncertain origin (see rugae).

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flounce (n.)

"deep ruffle on the skirt of a dress," 1713, from Middle English frounce "pleat, wrinkle, fold" (late 14c.), from Old French fronce "line, wrinkle; pucker, crease, fold," from Frankish *hrunkjan "to wrinkle," from Proto-Germanic *hrunk-, from PIE root *sker- (2) "to turn, bend." Influenced in form by flounce (v.). The verb meaning "arrange in flounces" is from 1711.

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rugae (n.)

1775, in zoology, anatomy, etc., "a fold or wrinkle," plural of ruga (1775), from Latin ruga "a wrinkle in the face," from Proto-Italic *rouga-, which is of uncertain origin. "Since words for 'wrinkle' and 'crease' are often derived from 'to be rugged', from which also 'to belch' is often derived ..., the most obvious connection is with e-rugere 'to belch'" [de Vaan].  Related: Rugate; rugulose; rugose (1703); rugosity (1590s).

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shrivel (v.)

1560s (implied in shriveled), a word of unknown origin, not found in Middle English; perhaps from a Scandinavian source (compare Swedish skryvla "to wrinkle, to shrivel"), perhaps ultimately connected with shrimp (n.) and shrink (v.). Related: Shriveled; shriveling.

Middle English did have rivelled "wrinkled, furrowed," from Old English rifelede, from *rifel "a wrinkle or fold on the skin," a word of obscure origin, "very common c 1530-1720" [OED] in the senses "dried" (of fruit), "shriveled by heat."

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frumpy (adj.)
1746, "cross-tempered," probably from the frumps (n.) "bad temper" (1660s) and an earlier verb meaning "to mock, browbeat" (1550s), of obscure origin, perhaps imitative of a sneer or derisive snort. See also frump. Sense of "sour-looking, unfashionable" is from 1825, but this may be a shortening of frumple "to wrinkle, crumple" (late 14c.), from Middle Dutch verrompelen "to wrinkle," from ver- "completely" + rompelen "to rumple." Related: Frumpily; frumpiness.
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