Rigid Motions and Similarity Transformations

Section 12-1

Activity Name	Activity Description
TransmoGrapher	Students input integer values used by the applet to translate, reflect and rotate a two-dimensional figure on the coordinate plane.
Floor Tiles	Students use a graphical interface to deform a square into a general quadrilateral tile pattern. Discussion can focus on the translations and rotations necessary to generate the pattern.
Tessellate!	Students use a graphical interface to deform regular polygons into complex interlocking tile patterns. Discussion can focus on the translations and rotations necessary to generate the pattern.
Slope Slider	Students use translations to manipulate the slope and intercept values of a linear function of the form f(x)=mx+b as plotted in the cartesian coordinate system. Discussion can focus on the translations or rotations necessary to change the slope vs. change the intercept of the line.
Hilbert Curve Generator	Students view a series of fractal Hilbert Curve patterns, created by a repeated process of replacing individual line segments with proportionally scaled and thus similar copies of the original modified shape.
Another Hilbert Curve Generator	Students view a series of fractal patterns of a curve similar to the Hilbert Curve, created by a repeated process of replacing individual line segments with proportionally scaled and thus similar copies of the original modified shape. The patterns can be compared to those of the Sierpinski Carpet.
Koch's Snowflake	Students view a series of fractal patterns known as the Koch Snowflake, created by a repeated process of replacing individual line segments with proportionally scaled and thus similar copies of the original modified segment.
Sierpinski's Triangle	Students view a series of fractal patterns known as the Sierpinski's Triangle, created by repeatedly subdividing the area of a triangle into proportional similar triangles.
Sierpinski's Carpet	Students view a series of fractal patterns known as the Sierpinski's Carpet, created by repeatedly subdividing the area of a square into proportional similar square sections. Results can be compared to 'Another Hilbert Curve'.
Fractal Dimensions	Students identify the scale (similarity) factor and 'number of copies' parameters from a geometric fractal pattern. The applet provides fractal images for successive iterations of each rule and calculates fractal dimension.
Fractured Pictures	Students input polygon and scale factors to generate geometric fractal patterns. The pattern is created with proportionally scaled and thus similar copies of the polygon.