New PDF release: 2d Curves

By Wassenaar J.

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Make now a line n parallel to l and m through Q. Then the point P of the curve is found by letting down a line down on n from point R. 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).

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' .

Notes 1) When the radius has the value zero, the circle is reduced to a single point, what is called a point circle. 2) Line PC bisects the angle APB. 3) The Egypt (1900 BC), the Mesopotamian (1700 BC), the Chinese and the Indian (500 BC). Struik 1977 chapter 2. 4) The value of pi is about 3,14159. ) = perimeter, contour. 6) The ultimate proof was given not earlier than in the second part of the 19th century, by Weierstrass. 7) To be compared with the sine. ) = two. 9) Davis 1981 p. 100. 10) Ku−klux is derived from the Greek word for circle: kyklos.

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2d Curves by Wassenaar J.


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