Etymology
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Words related to asymptote

a- (3)
prefix meaning "not, without," from Greek a-, an- "not" (the "alpha privative"), from PIE root *ne- "not" (source also of English un-).

In words from Greek, such as abysmal, adamant, amethyst; also partly nativized as a prefix of negation (asexual, amoral, agnostic). The ancient alpha privatum, denoting want or absence.

Greek also had an alpha copulativum, a- or ha-, expressing union or likeness, which is the a- expressing "together" in acolyte, acoustic, Adelphi, etc. It is from PIE root *sem- (1) "one; as one, together with."
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syn- 
word-forming element meaning "together with, jointly; alike; at the same time," also sometimes completive or intensive, from Greek syn (prep.) "with, together with, along with, in the company of," from PIE *ksun- "with" (source also of Russian so- "with, together," from Old Russian su(n)-). Assimilated to -l-, reduced to sy- before -s- and -z-, and altered to sym- before -b-, -m- and -p-. Since 1970s also with a sense of "synthetic."
*pet- 

Also petə-, Proto-Indo-European root meaning "to rush, to fly." 

It forms all or part of: accipiter; appetence; appetite; apterous; apteryx; archaeopteryx; asymptote; centripetal; Coleoptera; compete; competent; eurypterid; feather; helicopter; hippopotamus; Hymenoptera; impetigo; impetuous; impetus; iopterous; Lepidoptera; ornithopter; panache; panne; pen (n.1) "writing implement;" pennon; peripeteia; perpetual; perpetuity; petition; petulance; petulant; pin; pinion; pinnacle; pinnate; pinniped; potamo-; potamology; propitiation; propitious; ptero-; pterodactyl; ptomaine; ptosis; repeat; symptom.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit pattram "wing, feather, leaf," patara- "flying, fleeting;" Hittite pittar "wing;" Greek piptein "to fall," potamos "river, rushing water," pteron, pteryx "feather, wing," ptilon "soft feathers, down, plume;" Latin petere "to attack, assail; seek, strive after; ask for, beg; demand, require," penna "feather, wing;" Old Norse fjöðr, Old English feðer "feather;" Old Church Slavonic pero "feather;" Old Welsh eterin "bird."

asymptotic (adj.)
"having the characteristics of an asymptote," 1670s, see asymptote + -ic. Related: Asymptotical; asymptotically.