1.  half-moon(n = noun.body) lunula, lunule - the crescent-shaped area at the base of the human fingernail;
is a kind of area, region
is a part of nail

2.  half-moon(n = noun.time) - the time at which the Moon is at first or last quarter when half its face is illuminated;
is a kind of phase of the moon
is a part of month
has particulars: first quarter, last quarter

1.  The moon at the quarters, when half its disk appears illuminated. [1913 Webster]

2.  The shape of a half-moon; a crescent. [1913 Webster]
"See how in warlike muster they appear,
In rhombs, and wedges, and half-moons, and wings." [1913 Webster]

3.  An outwork composed of two faces, forming a salient angle whose gorge resembles a half-moon; -- now called a ravelin. [1913 Webster]

4.  A marine, sparoid, food fish of California (Cæsiosoma Californiense). The body is ovate, blackish above, blue or gray below. Called also medialuna. [1913 Webster]

N  curvature, curvity, curvation, incurvature, incurvity, incurvation, bend, flexure, flexion, flection, conflexure, crook, hook, bought, bending, deflection, deflexion, inflection, inflexion, concameration, arcuation, devexity, turn, deviation, detour, sweep, curl, curling, bough, recurvity, recurvation, sinuosity, kink, carve, arc, arch, arcade, vault, bow, crescent, half-moon, lunule, horseshoe, loop, crane neck, parabola, hyperbola, helix, spiral, catenary, festoon, conchoid, cardioid, caustic, tracery, arched ceiling, arched roof, bay window, bow window, sine curve, spline, spline curve, spline function, obliquity, curved, curviform, curvilineal, curvilinear, devex, devious, recurved, recurvous, crump, bowed, vaulted, hooked, falciform, falcated, semicircular, crescentic, sinusoid, parabolic, paraboloid, luniform, lunular, semilunar, conchoidal, helical, double helical, spiral, kinky, cordiform, cordated, cardioid, heart shaped, bell shaped, boat shaped, crescent shaped, lens shaped, moon shaped, oar shaped, shield shaped, sickle shaped, tongue shaped, pear shaped, fig shaped, kidney-shaped, reniform, lentiform, lenticular, bow-legged, oblique, circular, aduncated, arclike, arcuate, arched, beaked, bicorn, bicornuous, bicornute, clypeate, clypeiform, cymbiform, embowed, galeiform, hamate, hamiform, hamous, hooked, linguiform, lingulate, lobiform, lunate, navicular, peltate, remiform, rhamphoid, rostrate, rostriferous, rostroid, scutate, scaphoid, uncate, unguiculate, unguiform.