osculation

os·cu·la·tion

O0135700 (ŏs′kyə-lā′shən)n.1. a. The act of kissing.b. A kiss.2. Mathematics A contact, as between two curves or surfaces, at three or more common points.

os′cu·la·to′ry (ŏs′kyə-lə-tôr′ē) adj.

osculation

(ˌɒskjʊˈleɪʃən) n1. (Mathematics) maths Also called: tacnode a point at which two branches of a curve have a common tangent, each branch extending in both directions of the tangent2. rare the act or an instance of kissing osculatory adj

os•cu•la•tion

(ˌɒs kyəˈleɪ ʃən)

n. 1. the act of kissing. 2. kiss.

Thesaurus

Noun	1.	osculation - (mathematics) a contact of two curves (or two surfaces) at which they have a common tangentmath, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementcontact - the state or condition of touching or of being in immediate proximity; "litmus paper turns red on contact with an acid"
	2.	osculation - the act of caressing with the lips (or an instance thereof)buss, kisstouching, touch - the act of putting two things together with no space between them; "at his touch the room filled with lights"smooch, smack - an enthusiastic kissdeep kiss, French kiss, soul kiss - an openmouthed kiss in which your tongue is inserted into the other's mouth

osculation

nounThe act or an instance of kissing:buss, kiss, smack, smacker.Informal: peck.Slang: smooch.

Translations

ósculo

Osculation

The osculation of a curve q with a curve l at a given point M is a geometric concept meaning that q at M has contact with l of maximum order by comparison with the other curves in some preassigned family of curves {q} containing q.

Figure 1

The order of contact of q and l is n if the length of the segment QL is an infinitesimal of order n + 1 relative to the length of the segment MK (see Figure 1). Here, QL is perpendicular, when extended, to the common tangent of q and l at M. Thus, with respect to the curves in {q}, the curve that is closest to l—that is, the curve for which the length of QL is an infinitesimal of maximum order—is the osculating curve of l at M. For example, the osculating circle of l at M is the circle whose order of contact with l is greater than that of any other circle.

The osculation of a surface q belonging to a given family of surfaces {q} with some curve / or with some surface at the point M of the curve or surface can be defined in much the same way. The order of contact here is defined in a manner similar to the above. We need only replace the tangent line MK shown in Figure 1 by the tangent plane of q at M.

REFERENCES

La Vallée Poussin, C.-J. de. Kurs analiza beskonechno malykh, vol. 2. Leningrad-Moscow, 1933. (Translated from French.)
Il’in, V. A., and E. G. Pozniak. Osnovy matematicheskogo analiza, 3rd ed., part 1. Moscow, 1971.

osculation

noun

Synonyms for osculation

noun the act or an instance of kissing

Synonyms

buss
kiss
smack
smacker
peck
smooch

Synonyms for osculation

noun (mathematics) a contact of two curves (or two surfaces) at which they have a common tangent

Related Words

math
mathematics
maths
contact

noun the act of caressing with the lips (or an instance thereof)

Synonyms

buss
kiss

Related Words

touching
touch
smooch
smack
deep kiss
French kiss
soul kiss