By Wassenaar J.
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Extra info for 2D Curves
The group of scholars around Pythagoras had a special liking for numbers, which had for them a magical meaning. They studied the 'figure numbers' (or 'polygon numbers'), constructed from a regular polygon. In the following way, from a regular triangle: and so on. This results in the triangular numbers 1, 3, 6, 10, 15, and so on. In Pascal's triangle we find these same numbers als binomial coefficients (n over k) 1) : 1 1 1 1 1 1 1 2 3 4 5 1 3 6 10 4 10 1 1 5 1 These coefficients are often used in probability theory and also in formulae for the th th n power and the n derivative.
When we set the distance of the focus to the line to 1, we can write for a conic section with eccentricity e the polar equation at top of this page. In this equation it is quite clear that the polar inverse is the limaçon. The circular conic section is the circle. The orbit of a comet can in fact take the form of each of the conic sections. ) = cone circle conic section last updated: 2003−05−25 The circle is the ellipse of which the two axes are equal in length. Because of its symmetry the circle is considered as the perfect shape.
In other words: P has the x−coordinate of point R and the y−coordinate of point Q. It may be clear that not all resonance curves obey this construction rule. The curve is: • a projection of the horopter • the hyperbolism of the circle • resembling the transcendent Gauss curve The curve has been studied by Fermat (1666) and Grandi (1703). The Italian female mathematician Maria Gaetana Agnesi (1718−1799) wrote about the curve in her book 'Instituzioni analitiche (ad uso della gioventu italiana)' (1748).
2D Curves by Wassenaar J.