Van der Waals surface research use of a model showing the van der Waals surfaces of molecules. Related to the title concept are the ideas of a "van der Waals volume", V, and a "van der Waals surface area," abbreviated variously as A, vdWSA, VSA, and WSA. A van der Waals surface area is an abstract conception of the surface area of atoms or molecules from a mathematical estimation, either computing it from first principles or by integrating over a corresponding van der Waals volume. In simplest case, for a spherical monatomic gas, it is simply the computed surface area of a sphere of
Gabriel's Horn using Cavalieri's principle before the invention of calculus, but today calculus can be used to calculate the volume and surface area of the horn between and , where . Using integration (see Solid of revolution and Surface of revolution for details), it is possible to find the volume and the surface area : The surface area formula above gives a lower bound for the area as 2 times the natural logarithm of . There is no upper bound for the natural logarithm of as approaches infinity. That means, in this case, that the horn has an infinite surface area. That