the Earth–Moon distance. One may measure the distance between the closest points of the two objects; in this sense, the altitude of an airplane or spacecraft is its distance from the Earth. The same sense of distance is used in Euclidean geometry to define distance from a point to a line, distance from a point to a plane, or, more generally, perpendicular distance between affine subspaces. Even more generally, this idea can be used to define the distance between two subsets of a metric space. The distance between sets and is the infimum of the distances between any two of their respective points: This does not define a metric on the set of such subsets: the distance between overlapping sets is zero, and this distance does not satisfy the triangle inequality for any metric space with two or more points (consider the triple of sets consisting of two distinct singletons and their union). The Hausdorff distance between two subsets of a metric space can be thought of as measuring how far they are from perfectly overlapping. Somewhat more precisely, the Hausdorff distance between and is either the distance from to the farthest point of , or the distance from to the farthest point of , whichever is larger. (Here "farthest point" must be interpreted as a supremum.) The Hausdorff distance defines a metric on the set of compact subsets of a metric space. Related ideas The word distance is also used for related concepts that are not encompassed by the description "a numerical measurement of how far apart points or objects are". Distance travelled The distance travelled by an object is the length of a specific path travelled between two points, such as the distance walked while navigating a maze. This can even be a closed distance along a closed curve which starts and ends at the same point, such as a ball thrown straight up, or the Earth when it completes one orbit. This is formalized mathematically as the arc length of the curve. The distance travelled may also be signed: a "forward" distance is positive and a "backward" distance is negative. Circular distance is the distance traveled by a point on the circumference of a wheel, which can be useful to consider when designing vehicles or mechanical gears (see also odometry). The circumference of the wheel is ; if the radius is 1, each revolution of the wheel