Sketch the curve on a piece of graph paper. Imagine the line on the curved surface in a two-dimensional plane. Draw the curve using the grids on the graph paper as guidelines.
Draw a line segment for each consecutive set of coordinates. Starting at the far-left endpoint of the curve, plot a point where the curve intersects each vertical grid line.
Next connect the dots. Starting at the left endpoint, draw a straight line to the next intersection point on the right. From that new point, draw another line to the next point on the right. Continue until you reach the end of the curve. If you plotted 10 points on the curve, your curve will be subdivided into 10 straight line segments.
Calculate the distance between the endpoints of each line segment created. Use the distance formula for a line in two dimensions. First, find the differences between the x coordinates of the endpoints of the line segment. Then find the difference between the y coordinates of the endpoints of the line segment
For example, if the coordinates of the first line segment were (0, 1) and (1,4), the difference in the x coordinates would be 1 and the difference in the y coordinates would be.3.
Next square each of the two results. For this example, the result would be 1 and 9 because 1 squared is 1 and 3 squared is 9.
Then add these three results together. For this example, the result would be 10 because 1 plus 9 is 10.
Take the square root of this sum. The square root of 10 is 3.16. Repeat this procedure for all the line segments you have marked off.
Add together the distances of each line segment calculated. The total is the length of the curved line on the curved surface.