different between asymptote vs folium

English

Etymology

circa 1650, from Ancient Greek ????????? (asúmpt?t?), the feminine of Apollonius Pergaeus' (circa 200 BC) Ancient Greek adjective ?????????? (asúmpt?tos, “not falling together”), from ? (a, “not”) +? ??? (sún, “together”) +? ?????? (pt?tós, “fallen”).

Pronunciation

• (General American) IPA^(key): /?æs?mpto??t/, /?æs?mto??t/, /?e??s?mto??t/, /?æs?mt?t/

Noun

asymptote (plural asymptotes)

1. (mathematical analysis) A straight line which a curve approaches arbitrarily closely, as they go to infinity. The limit of the curve, its tangent "at infinity".
2. (by extension, figuratively) Anything which comes near to but never meets something else.
   • 1860: Frederic William Farrar, An Essay on the Origin of Language, page 117

     Language, in relation to thought, must ever be regarded as an asymptote.

Derived terms

Translations

Verb

asymptote (third-person singular simple present asymptotes, present participle asymptoting, simple past and past participle asymptoted)

1. (mathematical analysis) To approach, but never quite touch, a straight line, as something goes to infinity.
   • 2006: Neil deGrasse Tyson, The Perimeter of Ignorance

     As you become more scientific, yes, the religiosity drops off, but it asymptotes.

References

French

Etymology

Borrowed from Ancient Greek ?????????? (asúmpt?tos).

Pronunciation

• IPA^(key): /a.s??p.t?t/

Noun

asymptote f (plural asymptotes)

1. (mathematical analysis) asymptote

Derived terms

• asymptotique

Further reading

• “asymptote” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

English

Etymology

From Latin folium (“leaf”). Doublet of foil and folio.

Noun

folium (countable and uncountable, plural foliums or folia)

1. A leaf, especially a thin leaf or plate.
2. (geometry) A curve of the third order, consisting of two infinite branches having a common asymptote. The curve has a double point, and a leaf-shaped loop.
3. (uncountable) Synonym of turnsole (“purple dye”)

Latin

Etymology

From Proto-Indo-European *b?olh?yom (“leaf”), from *b?leh?- (“blossom, flower”). Alternatively from *d?olyom (*d?elh?- (“be green”)), whence Welsh dail and Middle Irish duille.

Pronunciation

• (Classical) IPA^(key): /?fo.li.um/, [?f?li???]
• (Ecclesiastical) IPA^(key): /?fo.li.um/, [?f??lium]

Noun

folium n (genitive foli? or fol?); second declension

1. a leaf
2. a petal
3. a sheet or leaf of paper
4. (figuratively) trifle, thing of no consequence

Declension

Second-declension noun (neuter).

¹Found in older Latin (until the Augustan Age).

Derived terms

Related terms

Descendants

References

• f?l?um in Charlton T. Lewis and Charles Short (1879) A Latin Dictionary, Oxford: Clarendon Press
• folium in Charlton T. Lewis (1891) An Elementary Latin Dictionary, New York: Harper & Brothers
• folium in Charles du Fresne du Cange’s Glossarium Mediæ et Infimæ Latinitatis (augmented edition, 1883–1887)
• f?l?um in Gaffiot, Félix (1934) Dictionnaire illustré Latin-Français, Hachette, page 678/1
• “folium” on page 719/3 of the Oxford Latin Dictionary (1st ed., 1968–82)
• Niermeyer, Jan Frederik (1976) , “folium”, in Mediae Latinitatis Lexicon Minus, Leiden, Boston: Brill, page 439/2