PerceptionPerception () is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information or environment. All perception involves signals that go through the nervous system, which in turn result from physical or chemical stimulation of the sensory system. Vision involves light striking the retina of the eye; smell is mediated by odor molecules; and hearing involves pressure waves.
Subjective constancySubjective constancy or perceptual constancy is the perception of an object or quality as constant even though our sensation of the object changes. While the physical characteristics of an object may not change, in an attempt to deal with the external world, the human perceptual system has mechanisms that adjust to the stimulus. There are several types of perceptual constancies in visual perception: Size constancy is one type of visual subjective constancy.
Cognitive scienceCognitive science is the interdisciplinary, scientific study of the mind and its processes with input from linguistics, psychology, neuroscience, philosophy, computer science/artificial intelligence, and anthropology. It examines the nature, the tasks, and the functions of cognition (in a broad sense). Cognitive scientists study intelligence and behavior, with a focus on how nervous systems represent, process, and transform information.
RotationRotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis.
Euler anglesThe Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in 3-dimensional linear algebra. Classic Euler angles usually take the inclination angle in such a way that zero degrees represent the vertical orientation. Alternative forms were later introduced by Peter Guthrie Tait and George H.
CognitionCognition is the "mental action or process of acquiring knowledge and understanding through thought, experience, and the senses". It encompasses all aspects of intellectual functions and processes such as: perception, attention, thought, imagination, intelligence, the formation of knowledge, memory and working memory, judgment and evaluation, reasoning and computation, problem-solving and decision-making, comprehension and production of language. Cognitive processes use existing knowledge and discover new knowledge.
Axis–angle representationIn mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction (geometry) of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the rotation about the axis. Only two numbers, not three, are needed to define the direction of a unit vector e rooted at the origin because the magnitude of e is constrained.
AngleIn Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays are also known as plane angles as they lie in the plane that contains the rays. Angles are also formed by the intersection of two planes; these are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Rotation formalisms in three dimensionsIn geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is described with the same tools, as it is defined as an imaginary rotation from a reference placement in space, rather than an actually observed rotation from a previous placement in space.
Angle trisectionAngle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge and a compass. In 1837, Pierre Wantzel proved that the problem, as stated, is impossible to solve for arbitrary angles. However, some special angles can be trisected: for example, it is trivial to trisect a right angle (that is, to construct an angle of 30 degrees).
