# Spiral of Semicircles Project

The following graphic generates spirals as follows. A semicircle of radius is drawn over the top of the axis from the point to . Then, if the number of semicircles is more than 1, another semicircle, this one of radius , is drawn from to . The spiral is continued by drawing connected semicircles, each with a radius reduced by a factor from the previous radius. Below are 3 problems you may be able to solve based on your knowledge of geometric series.

You can generate a random spiral (the words Spiral is Random will show on the graphic) or specify your own.
1. Find the total length of the spiral you generated.
2. Find the length of the spiral with the same value of and of the spiral from part 1 if infinitely many semicircles were generated.
3. Challenge problem: Find the coordinates of the single point on the x-axis that will be enclosed by every semicircle in the spiral, no matter how many are generated.