2023/09/14 by Akeroyd, John R., Powers, Robert K., Rao, Ganesh
#53 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2309.07647
The derivatives with respect to the variable r of πr2 and (4)/(3)πr3 are 2πr and 4πr2, respectively. This relates, through the derivative, the area enclosed in a circle to the length of that circle and, likewise, the volume of a sphere to the surface area of that sphere. The reasons why this works are basic to a first course in calculus. In this brief article, we expand on these ideas to shapes other than circles and spheres. Our approach is with the first year calculus student in mind.