Surface of revolution never negative, the area is given by If the curve is described by the function , , then the integral becomes for revolution around the -axis, and for revolution around the "y"-axis (using ). These come from the above formula. For example, the spherical surface with unit radius is generated by the curve , , when ranges over . Its area is therefore For the case of the spherical curve with radius , rotated about the -axis A minimal surface of revolution is the surface of revolution of the curve between two given points which minimizes surface area. A basic
Surface brightness photometric luminance and is therefore constant with distance: as an object becomes fainter with distance, it also becomes correspondingly smaller in visual area. In geometrical terms, for a nearby object emitting a given amount of light, radiative flux decreases with the square of the distance to the object, but the physical area corresponding to a given solid angle or visual area (e.g. 1 square arcsecond) decreases by the same proportion, resulting in the same surface brightness. For extended objects such as nebulae or galaxies, this allows the estimation of spatial distance from surface brightness by means of the distance modulus