Game theory

Game theory is the study of mathematical models of strategic interactions among people that always aims to perform optimal actions based on given premises and information. It has applications in all fields of social science, as well as in logic, systems science and computer science. ©Dreamstime In the 21st century, game theory applies to a wide range … Continue reading Game theory

Robot kinematics

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. A fundamental tool in robot … Continue reading Robot kinematics

Space in mathematics

Space is a set with some added structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. ©Wikipedia A space consists of selected mathematical objects that are treated as points, and selected relationships between these points. The nature of the points can vary … Continue reading Space in mathematics

Large Numbers

Large numbers  are significantly larger than those typically used in everyday life, for instance in simple counting or in monetary transactions, appear frequently in fields such as mathematics, cosmology, cryptography, and statistical mechanics. The term typically refers to large positive integers, or more generally, large positive real numbers, but it may also be used in other contexts. Sometimes, people refer to … Continue reading Large Numbers

Hyperbola

Hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three … Continue reading Hyperbola

Chaos Theory

Chaos theory is an interdisciplinary theory and branch of mathematics focusing on the study of chaos: dynamical systems whose apparently random states of disorder and irregularities are actually governed by underlying patterns and deterministic laws that are highly sensitive to initial conditions. Chaos theory states that within the apparent randomness of chaotic complex systems, there … Continue reading Chaos Theory

Poincaré conjecture

Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. The conjecture states: "Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere." Originally conjectured by Henri Poincaré, the theorem concerns a space that locally looks like ordinary three-dimensional space but is … Continue reading Poincaré conjecture