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.
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 ...
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)
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.
This is a list of Wikipedia articles about curves used in different fields: mathematics ... Involute; Isoptic including Orthoptic; Negative pedal curve. Fish 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.
The evolute of a hypocycloid is an enlarged version of the hypocycloid itself, while the involute of a hypocycloid is a reduced copy of itself. [10] The pedal of a hypocycloid with pole at the center of the hypocycloid is a rose curve. The isoptic of a hypocycloid is a hypocycloid.