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The image shows a pattern based on a regular 14-gon, and the task is to determine the smallest positive angle that produces rotational symmetry in this tiling.

For any regular polygon with \( n \) sides, the rotational symmetry occurs at angles of:

\[
\theta = \frac{360^\circ}{n}
\]

In this case, the regular polygon has 14 sides, so the smallest angle that produces symmetry is:

\[
\theta = \frac{360^\circ}{14} = 25.71^\circ
\]

Thus, the smallest positive angle that produces symmetry is **25.71°**.

Would you like a further breakdown of this concept or have any additional questions?

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Here are 5 relative questions to explore this further:

1. What is the general formula for finding rotational symmetry in polygons with different numbers of sides?
2. How does rotational symmetry differ from reflectional symmetry in polygons?
3. What is the importance of rotational symmetry in tiling patterns?
4. Can rotational symmetry be applied to irregular polygons?
5. How would the smallest angle change if the polygon had 12 sides instead of 14?

**Tip:** Symmetry in geometry often simplifies complex shapes and patterns, making them easier to analyze and manipulate mathematically.

The pattern below (based on a regular 14-gon) can be continued to tile the entire plane. This produces a tiling with rotational symmetry. What is the smallest positive angle which produces a symmetry? Write your answer correct to two decimal places.

Learn how to find the smallest positive angle that produces rotational symmetry in a tiling pattern based on a regular 14-gon. This problem involves key geometric concepts, such as rotational symmetry and polygon properties, using the formula θ = 360° / n.

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