Angle of Intersection for Equiangular Spirals

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The polar equation for an equiangular spiral is . You can vary the values of
,
, and
to see that the angle of intersection remains constant, independent of
. This means that, given arbitrary constants
and
, 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
.
Contributed by: Jason Kha (January 2015)
After work by: Robert M. Young
With additional contributions by: Vighnesh Souda
Open content licensed under CC BY-NC-SA
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Details
Reference
[1] R. M. Young, Excursions in Calculus: An Interplay of the Continuous and the Discrete, Washington, D.C.: Mathematical Association of America, 1992.
Permanent Citation
"Angle of Intersection for Equiangular Spirals"
http://demonstrations.wolfram.com/AngleOfIntersectionForEquiangularSpirals/
Wolfram Demonstrations Project
Published: January 21 2015