Saturday, January 14, 2012

Lemniscate

The equations $r^2=k^2\cos a\theta$ and $r^2=k^2\sin a\theta$ form the shape of lemniscate. If you take a look at the graph (in default setting) below, you might find out that there is no graph formed for $\theta = 90^o$ till $180^o$, and from $270^o$ to $360^o$. Can you explain why? You may drag the value of 'a' to see the difference of graphs and $\theta$ for the forming of the curve. Then, choose another equation to display its graph and compare. What can you say about these two graphs?

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Betty, Created with GeoGebra