In memoriam of Professor Irving Gottesman (1930-2016)

Overview

The two theorems developed by Pappus and Guldinus are widely used in mathematics, engineering, and physics to find the surface area and volume of any body of revolution. This is done by revolving a plane curve around an axis that does not intersect the curve to find its surface area or revolving a plane area around a non-intersecting axis to calculate its volume.
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.

Overview

Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...

GPCRs are primarily responsible for our sense of smell, taste, and vision.  The binding of a sensory stimulus activates GPCR to stimulate effector proteins, many of which are ion channels in the sensory organs. GPCRs modulate the opening and closing of the target ion channels either directly by binding them, or by releasing second messengers that activate these channels. As ions move across the membrane, the membrane potential is altered, which induces an appropriate response.
Sensory...