
06443533
j
2015d.00777
Skurnick, Ronald
Baderian, Armen
Javadi, Mohammad
Relating the interior of certain geometric figures to their boundary via differentiation.
Math. Comput. Educ. 49, No. 1, 3346 (2015).
2015
MATYC Journal, Old Bethpage, NY
EN
I40
I60
G30
G90
differential calculus
derivatives
plane geometry
solid geometry
$n$dimensional Euclidean space
convex regions
area
perimeter
volume
surface area
regular polygons
Platonic solids
inradius
circumradius
polygons
polyhedra
inscribed circles
circumscribed circles
inscribed spheres
circumscribed spheres
hyperspheres
From the text: When you take the derivative of the area of a circle with respect to its radius $r$, you get the circumference of the circle. Similarly, when you take the derivative of the volume of a sphere with respect to its radius $r$, you obtain the surface area of the sphere. As you may suspect, or already know, these two results are not coincidental, and can be explained using elementary geometric arguments. Perhaps the following presentation will be of interest to a mathematics club or an, individual student who has completed a year of calculus and has studied Euclidean plane and solid geometry, and trigonometry. In this article, we shall see that the above results are just two examples of a more general phenomenon.