Macchine Matematiche

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Toric sections - Strumento del Delaunay per tracciare le spiriche

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Toric sections
Strumento del Delaunay per tracciare le spiriche
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ABCD is an articulated rhombus with side AB=a and vertexes B and D forced to slide along the straight groove s. Rods PA and PB, linked in P, are the same length b, with b>a. Rod PQ is fixed to the wodden plane in point Q and forces P to draw circle y. When P moves along y , A and C together draw a quartic curve corresponding to y in a non-linear transformation. Varying the distance between Q and s Cassini's curves made of one or two ovals can be obtained. As a special case, the Leminscate is obtained when the distance between Q and s equals √((b2-a2) -r (r=radius of the circumference). All the curves traced by this machine can by secting a torus with plans parallel to its axes.

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a Torus with a plane parellel to the axis of rotation a spiric section is obtained. To define this curve, together with parameters r and d previously introduced, the distance p between thr Torus axis and the secant plane is needed.


 

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