**Up:** *The Shape of Space Curriculum Materials*

# Geodesics - Line of Sight

### The Shape of Space Curriculum Materials

### Objectives

- Students will be able to use tiled pictures to show a flatlander's
line-of-site.

### Materials

- Template A
- Colored pencils (6 color minimum), scissors, tape, straight edge

### Activity 1

- Cut out one square from Template A.
- With colored pencils and straight edge, draw straight lines connecting
A to each of the eight other points of the square. For best results,
lines with different slope should be colored a different color; lines with
the same slope should be colored the same color.
- Label each line with its correct slope. (Given: the slope of AD = 0,
and the slope of AB is undefined.)
- Circle the points
__in red__ which are out of the line of sight of
A.

### Activity 2

- Cut out a second square from Template A.
- Tape the second square to the left of the first square as shown:
- Draw lines connecting A or the copy of A to each of the other points
of either square. Lines with the same slope should be colored the same.
- Use the following table to list the different slopes drawn on the
figure.
__In blue__, circle all the points which are out of sight of A, or
the copy of A.

### Activity 3

- Cut out the top strip of the handout from Template A.
- What slopes through A, or a copy of A, would be possible?
- In a strip which has an infinite number of copies of the original
square, what slopes would be possible through any point A?
- What slopes through A would not lead to another point on the infinite
strip?
- With a partner, tape two strips together.
- What slopes through A are now possible?
- If there were an infinite number of infinite strips taped together,
make a generalization about the slope of the line passing through A and
any other point in this space.

**Up:** *The Shape of Space Curriculum Materials*

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