Etymology
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shape (n.)
Old English sceap, gesceap "form; created being, creature; creation; condition; sex, genitalia," from root of shape (v.)). Meaning "contours of the body" is attested from late 14c. Meaning "condition, state" is first recorded 1865, American English. In Middle English, the word in plural also had a sense of "a woman's private parts." Shape-shifter attested from 1820. Out of shape "not in proper shape" is from 1690s. Shapesmith "one who undertakes to improve the form of the body" was used in 1715.
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shape (v.)

Old English scapan, past participle of scieppan "to create, form, destine" (past tense scop), from Proto-Germanic *skapjanan "create, ordain" (source also of Old Norse skapa, Danish skabe, Old Saxon scapan, Old Frisian skeppa, Middle Dutch schappen "do, treat," Old High German scaffan, German schaffen "shape, create, produce"), from PIE root *(s)kep-, forming words meaning "to cut, scrape, hack" (see scabies), which acquired broad technical senses and in Germanic a specific sense of "to create."

Old English scieppan survived into Middle English as shippen, but shape emerged as a regular verb (with past tense shaped) by 1500s. The old past participle form shapen survives in misshapen. Middle English shepster (late 14c.) "dressmaker, female cutter-out," is literally "shape-ster," from Old English scieppan.

Meaning "to form in the mind" is from late 14c. Phrase Shape up (v.) is literally "to give form to by stiff or solid material;" attested from 1865 as "progress;" from 1938 as "reform;" shape up or ship out is attested from 1956, originally U.S. military slang, with the sense being "do right or get shipped up to active duty."

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concave (adj.)
Origin and meaning of concave

"incurved," early 15c., from Old French concave (14c.) or directly from Latin concavus "hollow, arched, vaulted, curved," from con-, here perhaps an intensive prefix (see con-), + cavus "hollow" (from PIE root *keue- "to swell," also "vault, hole").

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concavity (n.)

c. 1400, "a concave surface," from Old French concavit "hollow, concavity" (14c.) or directly from Latin concavitatem (nominative concavitas), from Latin concavus "hollow, arched, vaulted, curved," from con-, here perhaps an intensive prefix (see con-), + cavus "hollow" (from PIE root *keue- "to swell," also "vault, hole"). From 1570s as "state of being concave."

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castanet (n.)

usually castanets, "slightly concave shells of ivory or hard wood, fastened and used in beating time in music or dancing," 1640s, from French castagnette or directly from Spanish castañeta diminutive of castaña "chestnut," from Latin castanea (see chestnut).

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reshape (v.)

also re-shape, "shape anew, give a new shape to," 1798, from re- "again" + shape (v.). Related: Reshaped; reshaping.

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cromlech (n.)

"structure consisting of a large, flat, unhewn stone resting horizontally atop three or more upright ones," c. 1600, from Welsh, from crom, fem. of crwm "crooked, bent, concave" + llech "(flat) stone." Applied in Wales and Cornwall to what in Brittany is a dolmen; a cromlech there is part of a circle of standing stones.

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gouge (n.)
mid-14c., "chisel with a concave blade," from Old French gouge "a gouge" (14c.), from Late Latin gubia, alteration of gulbia "hollow beveled chisel," probably from Gaulish (compare Old Irish gulban "prick, prickle," Welsh gylfin "beak"). Meaning "an imposition, a cheat" is from 1845, American English colloquial.
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deform (v.)
Origin and meaning of deform

c. 1400, deformen, difformen, "to disfigure, mar the natural form or shape of," from Old French deformer (13c.) and directly from Latin deformare "put out of shape, disfigure," from de (see de-) + formare "to shape, fashion, build," also figurative, from forma "form, contour, figure, shape" (see form (n.)). Related: Deformed; deforming.

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shapely (adj.)
"well-formed, having a regular and pleasing shape," late 14c., from shape (n.) + -ly (1). Related: Shapeliness.
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