Origin and history of around

Middle English aboute, from Old English abutan (adv., prep.), earlier onbutan "on the outside of; around the circumference of, enveloping; in the vicinity of, near; hither and thither, from place to place," also "with a rotating or spinning motion," in late Old English "near in time, number, degree, etc., approximately;" a compound or contraction of on (see on; also see a- (1)) + be "by" (see by) + utan "outside," from ut (see out (adv.)).

By c. 1300 it had developed senses of "around, in a circular course, round and round; on every side, so as to surround; in every direction;" also "engaged in" (Wist ye not that I must be about my Father's business?), and gradually it forced out Old English ymbe, ymbutan (from PIE root *ambhi- "around") in the sense "round about, in the neighborhood of."

From mid-13c. as "in the matter, in connection with." From early 14c. as "in partial rotation, so as to face in a different direction." From late 14c. as "near at hand, about one's person." "In a circuitous course," hence "on the move" (late 13c.), and in Middle English "be about to do, be busy in preparation for," hence its use as a future participle in (to be) about to "in readiness, intending." Abouts (late 14c.), with adverbial genitive, still found in hereabouts, etc., probably is a northern dialectal form.

To bring about "cause or effect" and to come about "happen" are from late 14c. About face as a military command (short for right about face) is first attested 1861, American English.

c. 1300 (early 13c. as a surname), "spherical in shape; circular in outline," of persons or animals, "well-fed;" from Anglo-French rounde, Old French roont (12c., Modern French rond), probably originally *redond, from Vulgar Latin *retundus (source also of Provençal redon, Spanish redondo, Old Italian ritondo), from Latin rotundus "like a wheel, circular, round," related to rota "wheel" (see rotary). The French word is the source of Middle Dutch ront (Dutch rond), Middle High German runt (German rund) and similar words in the Germanic languages. 

As an adverb from c. 1300. As a preposition from c. 1600, "so as to make a complete circuit" (as in round the world); 1715 as "throughout, all through" (as in round the clock); by 1743 as "so as to make a turn or partial circuit about" (as in round the corner). In many cases it is a shortened form of around (adv.).

Of numbers from mid-14c., "entire, full, complete, brought to completion," with the notion of symmetry extended to that of completeness. Round number for one only approximately correct, usually expressed in 10s, 100s, etc., is by 1640s. Compare round (v.). Round trip "an outward and return journey" is by 1844, originally of railways. A round-dance (1520s) is one in which the dancers move in a circle or ring. Round heels attested from 1926, in reference to incompetent boxers, 1927 in reference to loose women, implying in either case a tendency to end up flat on one's back.