Download PDF by Wassenaar J.: 2D Curves

By Wassenaar J.

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Notes 1) In Pascal's 'Triangle aritmetique', published in 1764 (after Pascal's death), the relation between the binomial coefficients and Pascal's triangle is shown. 2) Some investigators doubt the mysterious character: it should be bad weather at time of those accidents, though. conic section main last updated: 2002−07−13 A conic section can be defined as the intersection of a plane and a conic, that's where the name is from. The relation between the angles of plane and conic determines the kind of conic section: • equal: parabola • smaller: ellipse; when the plane is parallel to the ground surface the resulting curve is a circle • larger: hyperbola These qualities were already known by Apollonius of Perga (200 BC).

The diverging parabola is the third 3 class. ' These divergent parabolas can be divided in the following species, depending on the solution on the right hand side of the equation: • three real roots: ♦ all roots equal: semi−cubic(al) parabola ♦ three real and unequal roots ♦ two equal roots: Tschirnhaus(en)'s cubic • just one real root Newton distinguished five species, taking account of the two forms of Tschirnhausen's cubic. semi−cubic(al) parabola As being a kind of a Newton's diverging parabola, it is the situation where the three real roots of the right hand equation are equal.

Folium of Descartes cubic last updated: 2002−03−25 The curve is is symmetric with respect to the line y = x, being a direct result of the polar equation: Descartes was the first to examine this curve, in 1638. He (incorrectly) believed that the shape was repeated in each quadrant. Roberval gave the curve the name of the fleur de jasmin, also the result of a incorrect understanding of the shape of the curve. This name was later replaced by the curve's existing name. 1) In French the curve is sometimes called the 'noeud de ruban' .

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2D Curves by Wassenaar J.


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