Geodesics path
Introduction:
Diagram 1- Official Diagram of the Mumbai Coastal Road, released by the Municipal Corporation of Greater Mumbai. A geodesic curve is the shortest possible path on a curved surface.
Geodesics Path on Curved surface
Volume and Surface area of Doughnut
The aim of the exploration is to derive an expression for the volume and surface area of a doughnut to find the bakery or food outlet, which provides the maximum volume and surface area per unit price.
I was looking for cost effective doughnut and hence I purchase doughnuts from different brand and calculated its volume and surface area. The doughnut with a greater surface area and greater volume for a lesser cost will be the optimal purchase.
Greater surface area will ensure greater coating of sugar or chocolate will be available. Greater volume for a lesser price would mean that I get to eat more content for a lesser price. Hence, I calculated the expression of the volume and surface area of a torus (donut) and later substitute the values for the bakery donuts for further evaluation.