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Serpentine Curve
A serpentine curve is a curve whose equation is of the form :x^2y+a^2y-abx=0, \quad ab > 0. Equivalently, it has a parametric representation :x=a\cot(t), y=b\sin (t)\cos(t), or functional representation :y=\frac. The curve has an inflection point at the origin. It has local extrema at x = \pm a, with a maximum value of y=b/2 and a minimum value of y=-b/2. History Serpentine curves were studied by L'Hôpital and Huygens, and named and classified by Newton. Visual appearance External links MathWorld – Serpentine Equation {{geometry-stub Plane curves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guillaume De L'Hôpital
Guillaume François Antoine, Marquis de l'Hôpital (; sometimes spelled L'Hospital; 1661 – 2 February 1704), also known as Guillaume-François-Antoine Marquis de l'Hôpital, Marquis de Sainte-Mesme, Comte d'Entremont, and Seigneur d'Ouques-la-Chaise, was a French mathematician. His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞. Although the rule did not originate with l'Hôpital, it appeared in print for the first time in his 1696 treatise on the infinitesimal calculus, entitled ''Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes''. This book was a first systematic exposition of differential calculus. Several editions and translations to other languages were published and it became a model for subsequent treatments of calculus. Biography L'Hôpital was born into a military family. His father was Anne-Alexandre de l'Hôpital, a Lieutenant-General of the King's army, Comte de Saint-Me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christiaan Huygens
Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists of all time and a major figure in the Scientific Revolution. In physics, Huygens made groundbreaking contributions in optics and mechanics, while as an astronomer he is chiefly known for his studies of the rings of Saturn and the discovery of its moon Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, a breakthrough in timekeeping and the most accurate timekeeper for almost 300 years. An exceptionally talented mathematician and physicist, Huygens was the first to idealize a physical problem by a set of mathematical parameters, and the first to fully mathematize a mechanistic explanation of an unobservable physical phenomenon.Dijksterhuis, F.J. (2008) Stevin, Huygens and the Dutch republ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the greatest mathematicians and physicists and among the most influential scientists of all time. He was a key figure in the philosophical revolution known as the Enlightenment. His book (''Mathematical Principles of Natural Philosophy''), first published in 1687, established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus. In the , Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity. Newton used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serpentine Curve
A serpentine curve is a curve whose equation is of the form :x^2y+a^2y-abx=0, \quad ab > 0. Equivalently, it has a parametric representation :x=a\cot(t), y=b\sin (t)\cos(t), or functional representation :y=\frac. The curve has an inflection point at the origin. It has local extrema at x = \pm a, with a maximum value of y=b/2 and a minimum value of y=-b/2. History Serpentine curves were studied by L'Hôpital and Huygens, and named and classified by Newton. Visual appearance External links MathWorld – Serpentine Equation {{geometry-stub Plane curves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
