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Introduction to Unit V- Transformations
What are transformations?
The word "transformation" refers
to a movement or change in a
geometric shape
Reflections
Definition: A reflection flips the object
across a point or line. An object and its
reflection have the same shape and size,
but the figures face in opposite
directions.
Example:
Reflections in Nature
Reflections in photography:
Horizontal Reflections
Select the upper part of the image, make a copy of it, flip it over vertically and line it up to the bottom of the upper image to make a perfect reflection.
Reflections in art: Vertical
Reflections
Reflections in Art
Vitruvian Man by Leonardo Divinci
Divinci regularly used math in his art. In fact, he said “Let
no one read me who is not a mathematician”
Translation
Definition: A translation moves an object
without changing its size or shape
and without turning it or flipping it.
So the object slides
Example: A person sliding down a water
slide
Translations in Architecture
How is this an example of a translation?
Where do you see reflections in this picture?
Translations in Art
M.C. Escher
Rotations
Definition: A rotation is a transformation
that turns a figure about a fixed point
called the center of rotation.
Characteristics: An object and its rotation
are the same shape and size, but the
figures may be turned in different
directions.
Examples of figures with rotational
symmetry
Rotations in Art
Carolina Lily
Islamic Art
Rosette Bearing the Name and Titles of the Emperor Shah Jahan
Mir 'Ali, Calligrapher
Doors, Pair, ca. 1325–1330; Mamluk period (1250-1517)
What other
transformation
do you see in
this picture?
Dilation
Definition: A dilation is a transformation
that produces an image that is the same
shape as the original, but is a different
size.
Example:
Examples of Dilations
Enlarged Multinucleate Cell
Line symmetry
Symmetry occurs when two halves of a figure mirror each other across a line. The line
of symmetry is the line that divides the figure into two mirror images. A simple test to
determine if a figure has line symmetry is to fold the figure along the supposed line of
symmetry and see if the two halves of the figure coincide.
Horizontal Line of symmetry
A piece of artwork with two lines of
symmetry
Lines of symmetry in geometric
figures
Broken Star
Point Symmetry/ Rotational
Symmetry
An object has rotational symmetry if there is a
center point around which the object is
turned (rotated) a certain number of degrees
and the object looks the same. A geometric
figure has rotational symmetry if the figure is the
image of itself under a rotation about a point
through any angle whose measure is strictly
between 0º and 360º. The angles of 0º and 360º
are excluded since nothing new happens.
Example: When you are riding on a ferris wheel, you are
rotating around the center of the ferris wheel