PLEASE HELP 1. Start by drawing a circle of diameter 1 with its center at the point (0,0) in the coordinate plane. What is the circumference of the circle? 2. Next, draw a square inside the circle so that the four vertices are on the circle and one of them is the point (1/2,0). What are the coordinates of the other points? Use the coordinates to find the length of one edge of the square. Then multiply by four to get perimeter of the square. Because the square is drawn using points on the circle, the perimeter of the square is an approximation to the circumference of the circle. Not a very good one, but it is an approximation of π . 3. To make our approximation better, we can use more sides to the polygon we draw inside the circle. Repeat part 2 using a regular pentagon. (You may need to look up some trig facts including how sine and cosine relate to coordinates of the points on the circle, or use the law of cosines). 4. To really make this useful, however, we need a way of getting as close as we want to the true value of π . Using the same ideas from part 3, find the formula for the perimeter of a regular n-gon (a regular polygon with n sides). 5. Use your formula from part 4 to get approximations to π using n = 10, n=100, and n=1000. [Use a calculator or computer algebra system that can provide a decimal representation with at least 10 digits; Sage, which you can access under the welcome module in Canvas, would be a good choice. In Sage, π is entered as pi, and the way to get a decimal representation of an exact value is using the n() function. For example, n(pi) will provide Sage's built-in approximation of π ]. 6. Although the approximations are getting closer each time, this particular approximation technique does not converge very quickly. To see this, look up the first ten decimal places of π [or use Sage's answer] and see how many decimal places your approximations using n=10, n=100, and n=1000 have correct. What value of n would you guess you need in order to satisfy NASA with your approximation?