Metric tensorIn the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold M (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there. More precisely, a metric tensor at a point p of M is a bilinear form defined on the tangent space at p (that is, a bilinear function that maps pairs of tangent vectors to real numbers), and a metric tensor on M consists of a metric tensor at each point p of M that varies smoothly with p.
Metric spaceIn mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane.
DysmetriaDysmetria (wrong length) is a lack of coordination of movement typified by the undershoot or overshoot of intended position with the hand, arm, leg, or eye. It is a type of ataxia. It can also include an inability to judge distance or scale. Hypermetria and hypometria are, respectively, overshooting and undershooting the intended position. Dysmetria is often found in individuals with multiple sclerosis (MS), amyotrophic lateral sclerosis (ALS), and persons who have had tumors or strokes.
Intention tremorIntention tremor is a dyskinetic disorder characterized by a broad, coarse, and low-frequency (below 5 Hz) tremor evident during deliberate and visually-guided movement (hence the name intention tremor). An intention tremor is usually perpendicular to the direction of movement. When experiencing an intention tremor, one often overshoots or undershoots one's target, a condition known as dysmetria. Intention tremor is the result of dysfunction of the cerebellum, particularly on the same side as the tremor in the lateral zone, which controls visually guided movements.
