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Everything about Osculating circle
Circle of immediate corresponding curvature of a curve at a point
An osculating circle is a circle that best approximates the curvature of a curve at a specific point. It is tangent to the curve at that point and has the same curvature as the curve at that point. The osculating circle provides a way to understand the local behavior of a curve and is commonly used in differential geometry and calculus. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Osculating circleA 5-minute orientation
- Skim a recent paper: Singular Surfaces of Osculating Circles in Three-Dimensional Euclidean SpaceInfluential work since 2022
- Pick up a classic book: Ten years at YaleThe most-reprinted book on the subject
- Read the landmark paper: OVERCOMING THE NEGATIVE FREQUENCIES - INSTANTANEOUS FREQUENCY AND AMPLITUDE ESTIMATION USING OSCULATING CIRCLE METHODCited 14 times
- Go sideways: CurvatureA closely related topic
- Go sideways: EllipseA closely related topic
📖 Definitions
Noun The circle that has the same tangent, and the same curvature at the point on the curve.
🏆 Landmark papers (most cited)
OVERCOMING THE NEGATIVE FREQUENCIES - INSTANTANEOUS FREQUENCY AND AMPLITUDE ESTIMATION USING OSCULATING CIRCLE METHOD
Surfaces of Osculating Circles in Euclidean Space
The Osculating Circle Without the Unit Normal Vector
Osculating Circle with Microscopes Within Microscopes
THE HIGHWAY SPIRAL AND THE OSCULATING CIRCLE*
Understanding Osculating Circle and Sphere: Modeling with Mathematica
On method of osculating circle for solving nonlinear equations
Dual quaternion-based osculating circle algorithm for finding intersection curves
🆕 Influential since 2022
📚 Books worth reading
Ten years at YaleGeorge Frederick Gundelfinger · 1915
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Ellipse In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of both distances to the two focal…
- Affine curvature Special affine curvature, also known as the equiaffine curvature or affine curvature, is a particular type of curvature that is defined on a plane curve…
- Centripetal force Centripetal force (from Latin centrum 'center' and petere 'to seek') is the force that makes a body follow a curved path. The direction of the centripetal…
- Radius of curvature In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best…
- Tangent lines to circles In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent…
- Principal curvature In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by…
- Parabola In mathematics, a parabola (/pəˈræbələ/ pə-RA-bə-lə) is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially…