in geometry, "a plane figure with numerous angles," 1570s, from Late Latin polygonum, from Greek polygōnon, noun use of neuter of adjective polygōnos "many-angled," from polys "many" (from PIE root *pele- (1) "to fill") + -gōnos "angled," from gōnia "angle, corner" (from PIE root *genu- (1) "knee; angle"). Related: Polygonal.

in geometry, "a plane figure having eight angles and eight sides," 1650s, from Latin octagonos, from Greek oktagōnos, literally "eight-angled, eight-cornered," from okta- combining form of okto "eight" (see eight) + gōnia "angle," which is related to gony "knee" (from PIE root *genu- (1) "knee; angle"). Also octogon (1650s), from French octogone.

"a salient angle or part, a projection," especially as part of a military work, 1828, from salient (adj.).

1530s, "corner, angle," from French canton "angle, corner (of a room); piece, portion of a country" (13c.), from Italian (Lombard dialect) cantone "region," especially in the mountains, augmentative of Latin canto "section of a country," literally "corner" (see cant (n.2)).

From 1570s as a term in heraldry and flag descriptions. From c. 1600 as "a subdivision of a country;" applied to the sovereign states of the Swiss republic from 1610s.

early 15c., "dull, blunted, not sharp," from Latin obtusus "blunted, dull," also used figuratively, past participle of obtundere "to beat against, make dull," from ob "in front of; against" (see ob-) + tundere "to beat," from PIE *(s)tud-e- "to beat, strike, push, thrust," from root *(s)teu- "to push, stick, knock, beat" (source also of Latin tudes "hammer," Sanskrit tudati "he thrusts"). Sense of "stupid, not acutely sensitive or perceptive" is by c. 1500. In geometry, in reference to a plane angle greater than a right angle," 1560s. Related: Obtusely; obtuseness.

Proto-Indo-European root meaning "knee; angle."

It forms all or part of: agonic; decagon; diagonal; geniculate; genuflect; genuflection; -gon; goniometer; heptagon; hexagon; knee; kneel; octagon; orthogonal; pentagon; polygon; trigonometry.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit janu, Avestan znum, Hittite genu "knee;" Greek gony "knee," gōnia "corner, angle;" Latin genu "knee;" Old English cneo, cneow "knee."

1622, originally in reference to the native people, later to the place in Rhode Island, from southern New England Algonquian Naiaganset "(people) of the small point of land," containing nai- "a point or angle."