This is a linear relationship. Compare this with the equation for a straight line: y=mx+b (4) If we choose to plot the circumference on the y-axis and the diameter on the x-axis, the slope (m) of such a graph will correspond to the value. In this case, we would expect the y-intercept (b) to be zero because a circle with a zero diameter would have a zero circumference. The slope of our graph will directly yield an accurate estimate of the mathematical constant (3.1415926). Seeing the linear relationship and being able to decide what to plot and what the slope means is very important. Enter your data into Excel and create a plot of the circumference versus the diameter for your measured circles (circumference will go on the y-axis). You should also put one extra data point into the table, (0,0). the diameter of nothing has a circumference of nothing. Add the best fit line and equation of the best fit line to the graph (If needed, rewatch the video on Blackboard about creating plots in Excel.) The number reported as "" is your slope. Just write it down. Then, the slope is your graphical estimate of as inferred from your experimental measurements of the circles. The slope m is my estimate for the value of n. 1. Did all of your data fall EXACTLY on the best fit line, or were there some small deviations apparent? What are these small deviations? 2. Were there any wildly deviant points? Perhaps these should be ignored or deleted from the table before the linear fit is made or could they be re-measured to check them! Human error is NEVER a part of the uncertainty in an experiment. Fix it, do it over, do it right. 3. What is the percent error of your experimental measurement (slope-m) of compared to the accepted value of the constant=3.14159? The general formula for percent error is: (measured value-accepted value) accepted value × 100% %error= For this experiment use: % error= (slope value-3.14159) 3.14159 x 100% Activity 3: Circles and Pi Collect 10 things that are circular shaped. For example, an old CD, a Bike tire, cups or plates, basketball, flower pots, a quarter, hula hoop, soup can, poker chip, barrel or frisbee. The LARGER range in diameters the items are, the better your results will be. Indicate the items used in your data table. Measure the diameter of each circular shape and record this information in Data Table 2. Measure the circumference of cach circular shape. It may be casier to roll it or to wrap a piece of string or a paper strip around the circle, marking the distance around. Then you can straighten the string or paper strip on a ruler to determine the total circumference. NOTE: If you are measuring something which is tapered, such as some drinking glasses, ensure you measure the circumference at exactly the same position you measure the diameter (e.g, at the rim or at the base). Data Table 2: Measurements of Circles Item Description Diameter D (mm) Circumference C (mm) 1 2 3 4 5 6 7 8 9 10 Circumference (C) and diameter (D) of a circle are related by a constant value (). C=D