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Consider the graph of r = theta for theta > 0 given in radians, also known as the Archimedean spiral. Prove that the intersections of this graph with the graph r = -theta are equidistant from each other. What is that distance?

Here's the picture of a few of these intersection points for a particular ray:
Note that we aren't including the origin as one of the intersections in the picture, since we aren't including the origin in the graph!

 
 May 15, 2024

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