osculate

Definitions

• WordNet 3.6
• v osculate touch with the lips or press the lips (against someone's mouth or other body part) as an expression of love, greeting, etc. "The newly married couple kissed","She kissed her grandfather on the forehead when she entered the room"
• v osculate have at least three points in common with "one curve osculates the other","these two surfaces osculate"
• v osculate be intermediate between two taxonomic groups "These species osculate"
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Webster's Revised Unabridged Dictionary
• Osculate (Biol) To have characters in common with two genera or families, so as to form a connecting link between them; to interosculate. See Osculant.
• Osculate To kiss one another; to kiss.
• Osculate To kiss.
• Osculate (Geom) To touch closely, so as to have a common curvature at the point of contact. See Osculation, 2.
• Osculate (Geom) To touch closely. See Osculation, 2.
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Century Dictionary and Cyclopedia
• osculate To salute with a kiss; kiss.
• osculate In geometry, to have a higher contact with; touch as closely as possible. Thus, a plane or a circle is said to osculate a curve when it has three coincident points in common with the curve — that is, it occupies such a position (and in the case of the circle has such a size) that as it is brought up into this position three points of intersection with the curve run into one. A sphere is said to osculate a tortuous curve when it has four coincident points in common with the curve. In these cases, to osculate means to have the greatest number of coincident and successive points common to a fixed locus which is compatible with the general character of the locus which osculates; and some geometers restrict the word to this meaning. This meaning is also extended to time: thus, the osculating elements of a planet are those elliptic elements which would satisfy three exact observations made at times infinitely little removed from a given epoch. But osculate is also used loosely to mean merely that the loci in question have three or more coincident points in common. A tangent-line or-plane is never said to osculate a curve or surface unless it has more than ordinary contact with it.
• osculate To kiss one another; kiss.
• osculate In geometry, to have, as two loci, three or more coincident and successive points in common. See I., 2.
• osculate In natural history, to share the characters of another group.
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Chambers's Twentieth Century Dictionary
• v.t Osculate to kiss: to touch, as two curves: to form a connecting-link between two genera
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Etymology

Webster's Revised Unabridged Dictionary
L. osculatus, p. p. of osculari, to kiss, fr. osculum, a little mouth, a kiss, dim. of os, mouth. See Oral, and cf. Oscillate
Chambers's Twentieth Century Dictionary
L. osculāri, -ātusosculum, a little mouth, a kiss, dim. of os, mouth.

Usage

In literature:

They would not understand our American habit of osculation.
"Where There's A Will" by Mary Roberts Rinehart
Tish says our vulgar lip-osculation is unknown in the Orient and that they rub noses by way of greeting.
"Tish, The Chronicle of Her Escapades and Excursions" by Mary Roberts Rinehart
If osculation is a mark of love, surely Mrs. Mack is the best of mothers.
"The Newcomes" by William Makepeace Thackeray
Then the crowns were removed and kissed by each of the marrying pair, the bridegroom first performing the osculation.
"Overland through Asia; Pictures of Siberian, Chinese, and Tartar Life" by Thomas Wallace Knox
When the children departed after an orgy of osculation, Jaffery surveyed with a twinkling eye the decorous quartette sitting by the fire.
"Jaffery" by William J. Locke
And still it kept slowly osculating.
"Fairy Tales Every Child Should Know" by Various
He hasn't osculated me once since I came.
"Clover" by Susan Coolidge
Osculant: intermediate in character between two groups or series.
"Explanation of Terms Used in Entomology" by John. B. Smith
The implant of the osculation was destined for her cheek.
"Fibble, D. D." by Irvin Shrewsbury Cobb
There were just a gross of osculations altogether.
"The Canterbury Puzzles" by Henry Ernest Dudeney
The long corridors were merry with affectionate osculations.
"Miss Ashton's New Pupil" by Mrs. S. S. Robbins
Whatever he projected in the nature of an enduring osculation was spoiled as Gladwin dropped the bag to the floor with a crash.
"Officer 666" by Barton W. Currie
She had bidden her patroness good morning, asked after her health, and received one of her temperate osculations.
"The Atlantic Monthly, Volume 15, No. 89, March, 1865" by Various
Kind words and the fragrant osculation had already saved him three dollars at his tailor's.
"Threads of Grey and Gold" by Myrtle Reed
Brisk osculation after the medicine.
"One Maid's Mischief" by George Manville Fenn
I suppose he was afraid she would have no lips left after such reiterated osculation.
"The Nibelungenlied" by Unknown
Out of the Egyptian darkness came the unmistakable sounds of osculation in various parts of the room.
"Excuse Me!" by Rupert Hughes
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In poetry:

But One there is more sage in that Caress,
Raising no mawkish Pennant of Distress,
But when I tip the Osculative Brim
Accepts the Kiss in Silent Thankfulness.
"The Rubáiyát of Omar Khayyám Jr." by Wallace Irwin
What mean those marks upon thee, girl?
Those prints of brutal osculation?
Great grief! that lowlife and that churl!
That Telephus abomination!
Can him, O votary of Venus,
Else everything is off between us.

In news:

So, you think you know osculation.
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In science:

RP2, and the osculating curve eK is given by the ﬂags (p, TpK ) where p runs through K .
Moduli spaces of convex projective structures on surfaces
It comes equipped with a continuous family of osculating lines.
Moduli spaces of convex projective structures on surfaces
The osculating curve provide the opposite arrow.
Moduli spaces of convex projective structures on surfaces
The functional space of osculating curves to smooth curves has a natural Poisson structure, the SL3 Gelfand-Dikii bracket.
Moduli spaces of convex projective structures on surfaces
Casimir operator (42) when the space-time has constant curvature or is an Einstein space, and reduces to (52) when it is ﬂat, and ii) it is osculator to the Laplacian operator.
Isometry germs and related structures
We call χ the twist angle, and take it as the angle between the osculating plane of CII and the y -axis (−π < χ 6 π).
The twisted arc model for chiral molecules
Cartoon to illustrate the difference between mean and osculating initial conditions with respect to the semi-ma jor axis (s.m.a.) evolution.
Global dynamics of high area-to-mass ratios GEO space debris by means of the MEGNO indicator
For the sake of simplicity, the mean semi-ma jor axis does not present any long-term variation, whereas the osculating semi-ma jor axis presents daily oscillations related to direct solar radiation pressure (the implicit underlying model is radiation pressure only).
Global dynamics of high area-to-mass ratios GEO space debris by means of the MEGNO indicator
More speciﬁcally, it is worth noting that, at ﬁrst, the sampling is carried out with respect to osculating initial conditions.
Global dynamics of high area-to-mass ratios GEO space debris by means of the MEGNO indicator
Figs. 1 and 2 reproduce the curve, the sextatic points, the osculating conic and the pro jective frame at t = π/4.
Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy
More complex topologies are possible, and indeed there is numerical evidence that the original outer horizons can osculate and then intersect each other76, allowing a self-intersecting inner horizon.
Dynamics of black holes
M0, the points P, Q of intersection with the osculating ellipse and the osculating parabola can be found.
Curvature Functionals for Curves in the Equi-Affine Plane
The ful l-aﬃne arc-length of the curve γ is precisely the pseudo-Riemannian arclength of its osculating parabolic congruence Pγ .
Curvature Functionals for Curves in the Equi-Affine Plane
As is clear from the left ﬁgure, not every curve in SL(2) can be realised as an osculating parabolic congruence from a curve in A2 .
Curvature Functionals for Curves in the Equi-Affine Plane
For indeed the unit tangent vector ﬁeld of such a hypothetical curve could only be horizontal, which would mean that the curve is a horizontal line, which does not admit osculating parabolas.
Curvature Functionals for Curves in the Equi-Affine Plane
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