Up: The Shape of Space Curriculum Materials

Geodesics - Line of Sight

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

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.

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.

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.

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