Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
Muscle contractionMuscle contraction is the activation of tension-generating sites within muscle cells. In physiology, muscle contraction does not necessarily mean muscle shortening because muscle tension can be produced without changes in muscle length, such as when holding something heavy in the same position. The termination of muscle contraction is followed by muscle relaxation, which is a return of the muscle fibers to their low tension-generating state.
Robot kinematicsIn robotics, robot kinematics applies geometry to the study of the movement of multi-degree of freedom kinematic chains that form the structure of robotic systems. The emphasis on geometry means that the links of the robot are modeled as rigid bodies and its joints are assumed to provide pure rotation or translation. Robot kinematics studies the relationship between the dimensions and connectivity of kinematic chains and the position, velocity and acceleration of each of the links in the robotic system, in order to plan and control movement and to compute actuator forces and torques.
MuscleMuscle is a soft tissue, one of the animal tissues that makes up the three different types of muscle. Muscle tissue gives skeletal muscles the ability to contract. Muscle is formed during embryonic development, in a process known as myogenesis. Muscle tissue contains special contractile proteins called actin and myosin which interact to cause movement. Among many other muscle proteins present are two regulatory proteins, troponin and tropomyosin. Muscle tissue varies with function and location in the body.
Non-Euclidean geometryIn mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries.
Euclidean geometryEuclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
Genu recurvatumGenu recurvatum is a deformity in the knee joint, so that the knee bends backwards. In this deformity, excessive extension occurs in the tibiofemoral joint. Genu recurvatum is also called knee hyperextension and back knee. This deformity is more common in women and people with familial ligamentous laxity. Hyperextension of the knee may be mild, moderate or severe. The normal range of motion (ROM) of the knee joint is from 0 to 135 degrees in an adult. Full knee extension should be no more than 10 degrees.
SprainA sprain is a soft tissue injury of the ligaments within a joint, often caused by a sudden movement abruptly forcing the joint to exceed its functional range of motion. Ligaments are tough, inelastic fibers made of collagen that connect two or more bones to form a joint and are important for joint stability and proprioception, which is the body's sense of limb position and movement. Sprains may be mild (first degree), moderate (second degree), or severe (third degree), with the latter two classes involving some degree of tearing of the ligament.
Elliptic geometryElliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry.
Computer simulationComputer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering.
