Ad
related to: examples of similarity words in geometry definitionkutasoftware.com has been visited by 10K+ users in the past month
Search results
Results from the WOW.Com Content Network
A similarity (also called a similarity transformation or similitude) of a Euclidean space is a bijection f from the space onto itself that multiplies all distances by the same positive real number r, so that for any two points x and y we have ((), ()) = (,), where d(x,y) is the Euclidean distance from x to y. [16]
3. Often used for denoting other types of similarity, for example, matrix similarity or similarity of geometric shapes. 4. Standard notation for an equivalence relation. 5. In probability and statistics, may specify the probability distribution of a random variable.
Similar to "canonical" but more specific, and which makes reference to a description (almost exclusively in the context of transformations) which holds independently of any choices. Though long used informally, this term has found a formal definition in category theory. pathological
In elementary geometry the word congruent is often used as follows. [2] The word equal is often used in place of congruent for these objects. Two line segments are congruent if they have the same length. Two angles are congruent if they have the same measure. Two circles are congruent if they have the same diameter.
A spiral similarity taking triangle ABC to triangle A'B'C'. Spiral similarity is a plane transformation in mathematics composed of a rotation and a dilation. [1] It is used widely in Euclidean geometry to facilitate the proofs of many theorems and other results in geometry, especially in mathematical competitions and olympiads.
Shapes may change if the object is scaled non-uniformly. For example, a sphere becomes an ellipsoid when scaled differently in the vertical and horizontal directions. In other words, preserving axes of symmetry (if they exist) is important for preserving shapes. Also, shape is determined by only the outer boundary of an object.
Exact self-similarity: identical at all scales, such as the Koch snowflake; Quasi self-similarity: approximates the same pattern at different scales; may contain small copies of the entire fractal in distorted and degenerate forms; e.g., the Mandelbrot set's satellites are approximations of the entire set, but not exact copies.
In the former case, equivalence of two definitions means that a mathematical object (for example, geometric body) satisfies one definition if and only if it satisfies the other definition. In the latter case, the meaning of equivalence (between two definitions of a structure) is more complicated, since a structure is more abstract than an object.
Ad
related to: examples of similarity words in geometry definitionkutasoftware.com has been visited by 10K+ users in the past month