Problem 42698. Why the heck are they blinking!?!?
Merry Christmas everyone! Sadly, the lights you've had on your tree for so many years burned out, and it's time to get a new set. Being a skilled (and cheap!) mathematician, you realize that you can estimate the total length of the strings of lights you'll need for your tree with two simple parameters:
- The radius of the base of the tree (in feet)
- The Number of rows of lights you want on your tree, from top to bottom.
The rows of lights are equally spaced vertically around the tree. Given these two variables, calculate how long your string of lights has to be in order to wrap around your tree. You want to buy the minimum possible length of lights, because NOBODY likes having to untangle any more lights than they have to!
Helpful hints - The answers calculated below model the lights on your tree as a two-dimensional Spiral of Archimedes, so the number of rows of lights is equal to the number of times your spiral makes a full 360-degree loop. The final Cartesian coordinate of your spiral should be (width, 0). If someone far smarter than I am wants to make the full three-dimensional version of this problem, knock yourself out!
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