Spiral of Semicircles Project
- Albert Navetta
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.
- Find the total length of the spiral you generated.
- Find the length of the spiral with the same value of and of the spiral from part 1 if infinitely many semicircles were generated.
- 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.