Ads
related to: inverse math definition geometry
Search results
Results from the WOW.Com Content Network
P ' is the inverse of P with respect to the circle. To invert a number in arithmetic usually means to take its reciprocal. A closely related idea in geometry is that of "inverting" a point. In the plane, the inverse of a point P with respect to a reference circle (Ø) with center O and radius r is a point P ', lying on the ray from O through P ...
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective , and if it exists, is denoted by f − 1 . {\displaystyle f^{-1}.}
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 inversive geometry, an inverse curve of a given curve C is the result of applying an inverse operation to C. Specifically, with respect to a fixed circle with center O and radius k the inverse of a point Q is the point P for which P lies on the ray OQ and OP·OQ = k 2. The inverse of the curve C is then the locus of P as Q runs over C.
Trigonometric functions of inverse trigonometric functions are tabulated below. A quick way to derive them is by considering the geometry of a right-angled triangle, with one side of length 1 and another side of length , then applying the Pythagorean theorem and definitions of the
A permutation's inversion set using place-based notation is the same as the inverse permutation's inversion set using element-based notation with the two components of each ordered pair exchanged. Likewise, a permutation's inversion set using element-based notation is the same as the inverse permutation's inversion set using place-based ...
Similarly, the inverse image (or preimage) of a given subset of the codomain is the set of all elements of that map to a member of . The image of the function f {\displaystyle f} is the set of all output values it may produce, that is, the image of X {\displaystyle X} .
In differential geometry, the inverse function theorem is used to show that the pre-image of a regular value under a smooth map is a manifold. [10] Indeed, let f : U → R r {\displaystyle f:U\to \mathbb {R} ^{r}} be such a smooth map from an open subset of R n {\displaystyle \mathbb {R} ^{n}} (since the result is local, there is no loss of ...
Ads
related to: inverse math definition geometry