Analytic geometry 3

The applets are started by clicking the red buttons.

Cycloids emerge as the paths traced out by the motion of points fixed on a disk which rolls on a stright line. This situation is illustrated in the applet. By means of two scroll bars, the disk can be moved and the position of the marked point relative to the center of the disk can be adjusted. The applet is started from the red button in its own window.

Logarithmic spirals are easily described and analyzed in terms of polar coordinates. They strengthen the feeling for exponential growth and admit applications of techniques corresponding to other subjects (in particular sequences, limiting processes and integration). Their geometry (to stretch a logarithmic spiral is equivalent to rotating it!) has amazed people for a long time. The applet is started from the red button in its own window.

Web hint:
  • Information about graphical representations of sixty famous curves and families of curves is provided by the pages Famous Curves by the School of Mathematical and Computational Sciences, University of St Andrews, Scotland. The curves may also be viewed as Java applets, in which the parameters may be changed interactively (see the Famous Curves Applet Index).

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