Search results
Results from the WOW.Com Content Network
In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve. [1] The evolute of an involute is the original curve.
Shannon's article laid out the basic elements of communication: An information source that produces a message; A transmitter that operates on the message to create a signal which can be sent through a channel; A channel, which is the medium over which the signal, carrying the information that composes the message, is sent
Involution (mathematics), a function that is its own inverse; Involution algebra, a *-algebra: a type of algebraic structure; Involute, a construction in the differential geometry of curves; Exponentiation (archaic use of the term)
Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...
In the case of communication of information over a noisy channel, this abstract concept was formalized in 1948 by Claude Shannon in a paper entitled A Mathematical Theory of Communication, in which information is thought of as a set of possible messages, and the goal is to send these messages over a noisy channel, and to have the receiver ...
A curve with a similar definition is the radial of a given curve. For each point on the curve take the vector from the point to the center of curvature and translate it so that it begins at the origin. Then the locus of points at the end of such vectors is called the radial of the curve.
In the case where the rolling curve is a line and the generator is a point on the line, the roulette is called an involute of the fixed curve. If the rolling curve is a circle and the fixed curve is a line then the roulette is a trochoid. If, in this case, the point lies on the circle then the roulette is a cycloid.
In mathematics, an involutory matrix is a square matrix that is its own inverse.That is, multiplication by the matrix is an involution if and only if =, where is the identity matrix.