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This applet illustrates the equiangular spiral given by the polar equation r=a eb θ.

The upper slider controls a and the middle slider controls b.

The bottom slider controls the direction of the red ray extending outward from the origin. Where this ray intersects the spiral, a tangent line to the spiral is shown. Notice that for a given spiral, the angle between the ray and the blue lines is constant. This is the "equiangular" property that give the spiral its name.

Try a nice small value for b and then move the ray around to see the multiple intersections.