This is the first i-Math in a four-part series of i-Maths entitled Symmetries and Their Properties. In this first i-Math you will investigate rotational symmetry. Fix a center, turn, and you have a rotation. Many objects in nature—flowers, starfish, and crystals—and objects we use every day, such as wheels, CDs, and drinking glasses, have rotational symmetry. Here, you will learn about the mathematical properties of rotations and have an opportunity to make your own designs.
Individual Lessons
Lesson 1 - Describing Rotations
Fix a center, turn, and you have a rotation. Many objects in nature—flowers, starfish, and crystals—and objects we use every day, such as wheels, CDs, and
drinking glasses, have rotational symmetry. The first thing to think about is how to describe a rotation mathematically.
Lesson 2 - Finding What Doesn't Change
Now that you have found out how to describe rotations of a figure, you can
predict the effect of a rotation through a given angle and even the effect of
two or more rotations performed one after the other. You will also be able to
find angles that leave a figure unchanged.
Lesson 3 - Relating Rotations to Symmetry
In this part, you will investigate the relationship between rotations and the symmetry you recognize in a figure or a design. This is the secret behind how
mathematicians describe symmetry. The figure rotates, but the figure does not appear to have moved. Mathematicians understand change by investigating what doesn't change. You will use this idea to find the rotations underlying various shapes and designs. We start with the rotations that describe cyclic symmetry in particular figures and designs. Look for what doesn't change!
Lesson 4 - Conclusions
We finish this 4-part i-Math Investigation on rotational symmetry by putting
things together. You will have the opportunity to think about the ideas you have
discovered in this i-Math as a whole by answering some review questions.
