test 4 Flashcards
A mapping of a metric space onto another or onto itself so that the distance between any two points in the original space is the same as the distance between their images in the second place
Isometries
Movement from one point of space to another such that every point of the figure moves in the same direction and over the same distance, without any rotation, reflection, or change in size
Translation
Circular movement around a center of axis
Rotation
“Flipping” of a figure about a particular point, segment, or line
Reflection
Reflection in a plane followed by translation using a vector parallel to the plane
Glide Reflection
Composition of two opposite isometries; transforming a shape without flipping it (preserves distance and orientation)
Direct Isometries
Transformation that changes the order of vertices; transforming a shape through flipping
Opposite Isometries
Having identical shapes and all parts corresponding to itself
Self-congruent
A rotation through x degrees
Rx
A reflection across a vertical line through the uppermost vertex
V
A reflection across a diagonal line through lower-left vertex
L
A reflection across a diagonal line through the lower-right vertex
R
A finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property
Group
Set of points on a plane
Figure
Shape is self-congruent after isometry
Symmetry
A set of numbers is closed under any arithmetic operation
Closure property
The sum or product of three or more numbers does not change based on grouping
Associative property
A number, the identity, can be added, subtracted, multiplied, or divided with another number and the result is always the other number
Identity property
Two numbers or properties that “undo” each other
Inverse property
Pattern that is infinite along one line
Frieze
Pattern that is infinite in two directions
Wallpaper pattern
Finite collection of polygon patterns that can be assembled to fill the plane completely
Semiregular
Penrose
Tiling
