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Curves and Volume

Curves and Volume. Pierre de Fermat (1601-1665) . Was a French Lawyer at the Parliament of Toulouse, France. Armature Mathematician credited for early developments that lead to infinitesimal calculus.

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Curves and Volume

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  1. CurvesandVolume

  2. Pierre de Fermat (1601-1665) • Was a French Lawyer at the Parliament of Toulouse, France • Armature Mathematician credited for early developments that lead to • infinitesimal calculus • In particular, he is recognized for his discovery of an original method of • finding the greatest and the smallest ordinates of curved lines, which is • similar to that of the then unknown differential calculus. • Mathematicians in the 17th century started looking at the area under • the curves. Pierre de Fermat generalised how to find the quadrature • of a parabola and hyperbola.

  3. finding slopes of curves What is infinitesimal calculus? Maxima Areas under curves Minima

  4. Conical Surface There are three types of conics. These are the ellipse, parabola, and hyperbola. The circle can also be considered as a fourth type but often comes under one of the three types above. Parabola is s a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. Given a point (the focus) and a corresponding line (the directrix) on the plane, the locus of points in that plane that are equidistant from them is a parabola Hyperbola In this case, the plane will intersect both halves (nappes) of the cone, producing two separate unbounded curves. Ellipse Arise when the intersection of cone and plane is a closed curve.

  5. Conical Surface Which is a parabola, hyperbola and ellipse?

  6. Volume In 1615 Kepler used the occasion of a practical problem to produce a theoretical treatise on the volumes of wine barrels. His StereometriaDoliorumVinariorum (“The Stereometry of Wine Barrels”) was the first book published in Linz. Kepler objected to the rule-of-thumb methods of wine merchants to estimate the liquid contents of a barrel. He also refused to be bound strictly by Archimedean methods; eventually he extended the range of cases in which a surface is generated by a conic section—a curve formed by the intersection of a plane and a cone rotating about its principal axis—by adding solids generated by rotation about lines in the plane of the conic section other than the principal axis

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