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25 relations: Arc length, Center of curvature, Circle packing theorem, Contact (mathematics), Curvature, Curve, Differential geometry of curves, Earth radius, Envelope (mathematics), Evolute, Frenet–Serret formulas, Gottfried Wilhelm Leibniz, Infinitesimal, Isaac Newton, Lissajous curve, Maxima and minima, Normal (geometry), Osculating curve, Osculating plane, Philosophiæ Naturalis Principia Mathematica, Radius of curvature, Tangent, Tangent circles, Tangent lines to circles, Vertex (curve).
Arc length
Determining the length of an irregular arc segment is also called rectification of a curve.
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Center of curvature
In geometry, the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal vector.
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Circle packing theorem
The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose interiors are disjoint.
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Contact (mathematics)
In mathematics, two functions have a contact of order k if, at a point P, they have the same value and k equal derivatives.
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Curvature
In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.
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Curve
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.
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Differential geometry of curves
Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus.
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Earth radius
Earth radius is the approximate distance from Earth's center to its surface, about.
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Envelope (mathematics)
In geometry, an envelope of a family of curves in the plane is a curve that is tangent to each member of the family at some point, and these points of tangency together form the whole envelope.
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Evolute
In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature.
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Frenet–Serret formulas
In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a continuous, differentiable curve in three-dimensional Euclidean space ℝ3, or the geometric properties of the curve itself irrespective of any motion.
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Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.
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Infinitesimal
In mathematics, infinitesimals are things so small that there is no way to measure them.
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Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.
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Lissajous curve
In mathematics, a Lissajous curve, also known as Lissajous figure or Bowditch curve, is the graph of a system of parametric equations which describe complex harmonic motion.
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Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
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Normal (geometry)
In geometry, a normal is an object such as a line or vector that is perpendicular to a given object.
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Osculating curve
In differential geometry, an osculating curve is a plane curve from a given family that has the highest possible order of contact with another curve.
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Osculating plane
In mathematics, particularly in differential geometry, an osculating plane is a plane in a Euclidean space or affine space which meets a submanifold at a point in such a way as to have a second order of contact at the point.
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Philosophiæ Naturalis Principia Mathematica
Philosophiæ Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy), often referred to as simply the Principia, is a work in three books by Isaac Newton, in Latin, first published 5 July 1687.
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Radius of curvature
In differential geometry, the radius of curvature,, is the reciprocal of the curvature.
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Tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.
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Tangent circles
In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point.
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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.
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Vertex (curve)
In the geometry of planar curves, a vertex is a point of where the first derivative of curvature is zero.
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Redirects here:
Circle of curvature, Circle of osculation, Kissing circles.
References
[1] https://en.wikipedia.org/wiki/Osculating_circle
