Spiric sections | Algebraic curves | Plane curves
In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2c from each other as the locus of points P so that PF1·PF2 = c2. The curve has a shape similar to the numeral 8 and to the ∞ symbol. Its name is from lemniscatus, which is Latin for "decorated with hanging ribbons". It is a special case of the Cassini oval and is a rational algebraic curve of degree 4. This lemniscate was first described in 1694 by Jakob Bernoulli as a modification of an ellipse, which is the locus of points for which the sum of the distances to each of two fixed focal points is a constant. A Cassini oval, by contrast, is the locus of points for which the product of these distances is constant. In the case where the curve passes through the point midway between the foci, the oval is a lemniscate of Bernoulli. This curve can be obtained as the inverse transform of a hyperbola, with the inversion circle centered at the center of the hyperbola (bisector of its two foci). It may also be drawn by a mechanical linkage in the form of Watt's linkage, with the lengths of the three bars of the linkage and the distance between its endpoints chosen to form a crossed parallelogram. (Wikipedia).
Lagrange Bicentenary - Jacques Laskar's conference
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From playlist Bicentenaire Joseph-Louis Lagrange
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From playlist Bicentenaire Joseph-Louis Lagrange
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From playlist Bicentenaire Joseph-Louis Lagrange
il Large Hadron Collider (Italiano)
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From playlist Italiano
B24 Introduction to the Bernoulli Equation
The Bernoulli equation follows from a linear equation in standard form.
From playlist Differential Equations
Newton's method and algebraic curves | Real numbers and limits Math Foundations 86 | N J Wildberger
Newton's method can be extended to meets of algebraic curves. We show how, using the examples of the Fermat curve and the Lemniscate of Bernoulli. We start by finding the Taylor expansions of the associated polynomials (polynumbers) at a fixed point (r,s) in the plane. The first tangents
From playlist Math Foundations
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This video introduces some key objects, and also challenges, when we move beyond the Greek tradition to the more modern view of "curves". This rests crucially on the development of analytic geometry, or Cartesian coordinates, by Fermat and Descartes in the 17th century. They, along with Jo
From playlist Algebraic Calculus One from Wild Egg
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From playlist Applied Math
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From playlist Differential Geometry
Parametrized curves and algebraic curves | Differential Geometry 3 | NJ Wildberger
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From playlist Differential Geometry
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Sylvie Benzoni, mathématicienne et directrice de l'IHP, vous fait visiter le bâtiment Perrin, sur le campus Curie dans le cinquième arrondissement de Paris. Ce bâtiment est en cours de réhabilitation pour accueillir en 2021 des espaces d'accueil pour la communauté internationale de recherc
From playlist Visite virtuelle de la Maison Poincaré
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From playlist MathHistory: A course in the History of Mathematics
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From playlist Math Foundations
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La Maison Poincaré - Visite virtuelle
Sylvie Benzoni, mathématicienne et directrice de l'IHP, vous fait visiter le bâtiment Perrin, sur le campus Curie dans le cinquième arrondissement de Paris. Ce bâtiment est en cours de réhabilitation pour accueillir en 2021 des espaces d'accueil pour la communauté internationale de recherc
From playlist Visite virtuelle de la Maison Poincaré
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Visit http://ilectureonline.com for more math and science lectures! In this video I will graph polar equation r^2=(2^2)[cos2(theta)], the lemniscate. Next video in the polar coordinates series can be seen at: http://youtu.be/WzlQjURlikE
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From playlist Bibliothèque