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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Reference

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



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