## An Equiangular SpiralAn equiangular
spiral, also known as a logarithmic
spiral is a curve
with the property that the angle α
between the tangent and the
radius at any point of the spiral is constant. In parametric form: x(t)=ae The slider t
allows us to change the parameter. - Move the random point R over the spiral to see the constant angle α between the radius and the tangent.
- Use the sliders a and b to study the way they control the spiral.
- Consider a>0; a<0, b>0, b<0, b=0 and very large values of b.
Irina Boyadzhiev, Created with GeoGebra Note: this construction is using the real constant b in the polar equation of the spiral as a slider parameter. |

The following construction is very similar to the construction above. The difference is that the control b is replaced by the angle α - Move the random point R over the spiral to see the constant angle α between the radius and the tangent.
- Use the sliders a and α to study the way they control the spiral.
- Consider a>0; a<0; α>90°, α<90°, α=90°.
Irina Boyadzhiev, Created with GeoGebra |