Angle of Intersection for Equiangular Spirals

a

1.6

b

1

θ

6

angle of intersection

72.9676°

The polar equation for an equiangular spiral is

r=a

bθ

e

. You can vary the values of

a

,

b

, and

θ

to see that the angle of intersection remains constant, independent of

θ

. This means that, given arbitrary constants

a

and

b

, the acute angle formed between any radial vector to a point on the curve and the tangent line to the curve at that point remains the same for all values of

θ

.

References

[1] R. M. Young, Excursions in Calculus: An Interplay of the Continuous and the Discrete, Washington, D.C.: Mathematical Association of America, 1992.

External Links

Logarithmic Spiral (Wolfram MathWorld)

Permanent Citation

Jason Kha, Robert M. Young, Vighnesh Souda

"Angle of Intersection for Equiangular Spirals"
http://demonstrations.wolfram.com/AngleOfIntersectionForEquiangularSpirals/
Wolfram Demonstrations Project
Published: January 21, 2015