Definition of Osculating circle

1. Noun. The circle that touches a curve (on the concave side) and whose radius is the radius of curvature.

Exact synonyms: Circle Of Curvature
Generic synonyms: Circle



Definition of Osculating circle

1. Noun. (mathematics for any point on a curve) The circle that has the same tangent, and the same curvature at the point on the curve ¹

¹ Source: wiktionary.com

Osculating Circle Pictures

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Lexicographical Neighbors of Osculating Circle

oscitant
oscitantly
oscitate
oscitated
oscitates
oscitating
oscitation
oscitations
oscula
osculant
oscular
osculate
osculated
osculates
osculating
osculating circle (current term)
osculating orbit
osculation
osculations
osculator
osculatories
osculators
osculatory
osculatrices
osculatrix
oscule
oscules
osculum
ose
oseltamivir

Literary usage of Osculating circle

Below you will find example usage of this term as found in modern and/or classical literature:

1. A Treatise on Conic Sections: Containing an Account of Some of the Most by George Salmon (1879)
"This construction shows that the osculating circle at either vertex has a ... Find the coordinates of the point where the osculating circle meets the conic ..."

2. An Elementary Course of Infinitesimal Calculus by Horace Lamb (1897)
"osculating circle. A slightly different way of treating the matter is based on the notion of the ' osculating circle.' If Q and R be two neighbouring points ..."

3. Elements of Quaternions by William Rowan Hamilton (1866)
"An osculating circle to a curve of double curvature does not generally meet that curve again; but it intersects generally a plane curve, of the degree n, ..."

4. Proceedings of the London Mathematical Society by London Mathematical Society (1905)
"(3) The osculating circle at a fixed point B of a spherical 4-ic meets the curve again in A ; and on any circle meeting the curve in A, H, B, ..."

5. Elements of the Integral Calculus: With a Key to the Solution of by William Elwood Byerly, Benjamin Osgood Peirce (1895)
"A circle tangent to a curve at any point, and having the same curvature as the curve at that point, is called the osculating circle of the curve at the ..."

6. Differential and Integral Calculus by Daniel Alexander Murray (1908)
"osculating circle. It was pointed out in Art. 95, Note 3, that contact of the second order is, in general, the closest contact that a circle can have with a ..."

7. A First Course in the Differential and Integral Calculus by William Fogg Osgood (1922)
"The osculating circle. At an arbitrary point P of a curve let the normal be drawn toward ... It is called the osculating circle and has the property that it ..."

8. Elements of the Differential Calculus: With Examples and Applications : a by William Elwood Byerly (1901)
"osculating circle. Ans. x = — 90. As the curvature of a circle has been found to be the reciprocal of its radius, a circle may be drawn which shall have any ..."

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