http://www.mi.sanu.ac.rs/vismath/jadrbookhtml/part03.html
Isometry
n.
1. Equality of measure.
2. Equality of elevation above sea level.
3. Mathematics A function between metric spaces which preserves distances, such as a rotation or translation in a plane.
n
1. (Mathematics) Maths rigid motion of a plane or space such that the distance between any two points before and after this motion is unaltered
2. (Earth Sciences / Physical Geography) equality of height above sea level
1. Equality of measure.
2. Equality of elevation above sea level.
3. A function between two metric spaces (such as two coordinate systems) which preserves distances. A rotation or translation in a plane is an isometry, since the distances between two points on the plane remain the same after the rotation or translation.
Metric
Mathematics A geometric function that describes the distances between pairs of points in a space.
(Mathematics) Maths denoting or relating to a set containing pairs of points for each of which a non-negative real number ρ(x, y) (the distance) can be defined, satisfying specific conditions
a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
The first steps in the development of the theory of symmetry in the 18th century stem from basic isometric transformations - mirror reflections
A typical example of isometric transformation (transformation of congruence
Isometry
n.
1. Equality of measure.
2. Equality of elevation above sea level.
3. Mathematics A function between metric spaces which preserves distances, such as a rotation or translation in a plane.
n
1. (Mathematics) Maths rigid motion of a plane or space such that the distance between any two points before and after this motion is unaltered
2. (Earth Sciences / Physical Geography) equality of height above sea level
1. Equality of measure.
2. Equality of elevation above sea level.
3. A function between two metric spaces (such as two coordinate systems) which preserves distances. A rotation or translation in a plane is an isometry, since the distances between two points on the plane remain the same after the rotation or translation.
Metric
Mathematics A geometric function that describes the distances between pairs of points in a space.
(Mathematics) Maths denoting or relating to a set containing pairs of points for each of which a non-negative real number ρ(x, y) (the distance) can be defined, satisfying specific conditions
a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
The first steps in the development of the theory of symmetry in the 18th century stem from basic isometric transformations - mirror reflections
A typical example of isometric transformation (transformation of congruence
Their combinations create all kinds of plane isometric transformations (transformations of congruence, or simply, isometries). Geometric transformation is an isometry (transformation of congruence) if it preserves the distance (metrics), i.e., if each pair of points X and Y are transformed into points X1 and Y1 in such a way that the distance between points X and Y is congruent to the distance between X1 and Y1 (Lopandic, 1979, Martin, 1982). This means that for every pair of the points X,Y and their images X1=t(X), Y1=t(Y) holds XY @ X1Y1. A typical example of isometric transformation (transformation of congruence) is the physical motion of a solid, where the distance between any two of its points remains unchanged (congruent) and consequently, the whole solid itself remains unchanged. However, the motion of fluids (for example, the vapor in clouds) does not have this characteristic.
No comments:
Post a Comment