Complete parts a and b below. a. How many reflection symmetries does a five-pointed star have? How many rotational symmetries does a five-pointed star have? b. How many reflection symmetries does a fourteen-pointed star have? How many rotational symmetries does a fourteen-pointed a. star have? b. The five-pointed star has reflection symmetries and rotational symmetries.
Complete parts a and b below. a. How many reflection symmetries does a five-pointed star have? How many rotational symmetries does a five-pointed star have? b. How many reflection symmetries does a fourteen-pointed star have? How many rotational symmetries does a fourteen-pointed a. star have? b. The five-pointed star has reflection symmetries and rotational symmetries.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Symmetry and Rotation in Stars
#### Complete parts a and b below.
a. **How many reflection symmetries does a five-pointed star have? How many rotational symmetries does a five-pointed star have?**
- **Diagram (a)**: This diagram shows a five-pointed star.
b. **How many reflection symmetries does a fourteen-pointed star have? How many rotational symmetries does a fourteen-pointed star have?**
- **Diagram (b)**: This diagram shows a fourteen-pointed star.
---
**Reflection and Rotational Symmetries**
Complete the following statement:
```
The five-pointed star has [] reflection symmetries and [] rotational symmetries.
```
---
### Explanation of the Diagrams:
- **Diagram (a)**:
- This shows a five-pointed star, which is a common example used to study symmetry. This shape can be reflected across its lines of symmetry and can also be rotated around its center.
- **Diagram (b)**:
- This shows a fourteen-pointed star, which provides a more complex example for studying symmetry. This shape also has lines of reflection symmetry and rotational symmetry.
### Key Definitions:
- **Reflection Symmetry**: When a shape or figure can be divided into two identical halves that are mirror images of each other.
- **Rotational Symmetry**: When a shape or figure can be rotated (less than a full circle) about its center and still look exactly the same.
Please fill in the blank squares with the appropriate numbers reflecting the symmetries of the five-pointed star.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f07f1fc-c1c5-43de-ad13-01ae8930f316%2F92a15f3f-f143-43c7-abf4-df828a781c99%2Fj5rwifo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Symmetry and Rotation in Stars
#### Complete parts a and b below.
a. **How many reflection symmetries does a five-pointed star have? How many rotational symmetries does a five-pointed star have?**
- **Diagram (a)**: This diagram shows a five-pointed star.
b. **How many reflection symmetries does a fourteen-pointed star have? How many rotational symmetries does a fourteen-pointed star have?**
- **Diagram (b)**: This diagram shows a fourteen-pointed star.
---
**Reflection and Rotational Symmetries**
Complete the following statement:
```
The five-pointed star has [] reflection symmetries and [] rotational symmetries.
```
---
### Explanation of the Diagrams:
- **Diagram (a)**:
- This shows a five-pointed star, which is a common example used to study symmetry. This shape can be reflected across its lines of symmetry and can also be rotated around its center.
- **Diagram (b)**:
- This shows a fourteen-pointed star, which provides a more complex example for studying symmetry. This shape also has lines of reflection symmetry and rotational symmetry.
### Key Definitions:
- **Reflection Symmetry**: When a shape or figure can be divided into two identical halves that are mirror images of each other.
- **Rotational Symmetry**: When a shape or figure can be rotated (less than a full circle) about its center and still look exactly the same.
Please fill in the blank squares with the appropriate numbers reflecting the symmetries of the five-pointed star.
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