Question

for exercise 8, answer the question.

1. stem connection all snowflakes can be created using rotations. by folding a piece of paper with a center of rotation, and creating a design, you can create a snowflake. describe how rotations were used to create the paper snowflake shown.

Explanation:

1. First, identify the center of rotation (the central point of the snowflake).
2. The snowflake has 6 - fold symmetry (common in snowflakes). So, the basic design (from the folded paper, likely a triangular - shaped design as seen in the image) is rotated around the center.
3. The angle of each rotation is calculated as $\frac{360^{\circ}}{n}$, where $n = 6$ (for 6 - fold symmetry), so each rotation is $60^{\circ}$.
4. Start with the original design (the triangular cut - out). Rotate this design $60^{\circ}$ around the center, then another $60^{\circ}$ (total $120^{\circ}$ from the original), and so on, until we have made 5 rotations (since starting with the original, 6 total positions including the original give the full snowflake). Each rotation maps the previous design onto a new position, and when combined, they form the complete snowflake with 6 identical arms.

Answer:

The snowflake has 6 - fold rotational symmetry. The basic triangular design (from the folded paper) is rotated around the center of the snowflake. The angle of each rotation is $\boldsymbol{60^{\circ}}$ (since $\frac{360^{\circ}}{6}=60^{\circ}$). Starting with the original triangular design, we rotate it $60^{\circ}$ around the center, then another $60^{\circ}$ (total $120^{\circ}$ from the original), and repeat this process 5 times (for a total of 6 positions including the original). Each rotation maps the design to a new position, and together these rotated copies form the complete snowflake with 6 identical - looking arms.