An isometry is a transformation in geometry that preserves distances between points, meaning the original shape and the transformed shape are congruent. Isometries include translations, rotations, reflections, and glide reflections, and are fundamental in understanding symmetry and rigid motions in Euclidean spaces.

Isometry

isometry

transformation in geometry

preserves distances

original shape

transformed shape

congruent

translations

Rotations are transformations that turn a figure around a fixed point, maintaining the figure's size and shape. They are fundamental in understanding symmetry, geometry, and various applications in physics and engineering.

rotations

Reflections occur when light waves encounter a surface and are returned to the medium from which they originated. This phenomenon is fundamental in optics and has diverse applications, from everyday mirrors to advanced scientific instruments.

reflections

glide reflections

understanding symmetry

rigid motions

Euclidean spaces are fundamental constructs in mathematics that generalize the notion of two-dimensional and three-dimensional spaces to any finite number of dimensions, characterized by the Euclidean distance formula. They form the basis for much of geometry and are essential in fields such as physics, computer science, and engineering for modeling and solving real-world problems.

Euclidean spaces

Understanding Isometric Transformations in Geometry

Types of Rigid Motions

Properties of Inner Products

Relevant Degrees

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