I wonder why they chose 3.05 instead of just 3. The best I could come up with is related to a student using the inscribed n-gon method for computing a lower bo

I wonder why they chose 3.05 instead of just 3. The best I could come up with is related to a student using the inscribed n-gon method for computing a lower bound. The two obvious choices for an inscribed n-gon are a 6-gon and a 12-gon. Computing their perimeters involves computing cos(pi/3) or cos(pi/6) respectivly. Both of these are generally found the same way. By bisecting an equalateral triangle, you get a right angle triangle with angles pi/3 and pi/6, from which sin/cos/tan can easily be read. Once you have the relevent cos, it is straightforward trig and algebra to find With a 6-gon: pi>3 With a 12-gon: pi>6sqrt(2-sqrt(3)) Using a calculator, the 12-gon lower bound is pi>3.1058... Computing by hand (which I did), you end up having enough wiggle room to get away with some further approximations; but still need to go through some somewhat tedious computation. Maybe they were concerned that some students solution for pi>3 that I didn't, but as far as I have been able to see, the extra .05 just makes the problem more messy.