TEACHING INTEGRATED
MATHEMATICS AND SCIENCE



ACTIVITY 1


PROOF THAT THE EARTH IS SPHERICAL



OBJECTIVE:

To use indirect evidence as a means of verifying that the earth is a spherical body in space.

MATERIALS:

a cube, such as a child's building block
a rectangular block of wood or other ridgid material
a cylinder such as a can of soup
a cone such as the sugar cones used for ice cream
a tennis ball (or any other kind of ball)
a slide, filmstrip, or overhead projector
a projection screen or light colored wall


INTRODUCTION:

Cosmologies from widely separated ancient cultures often had a description of the Earth and its general place in the scheme of the universe. These descriptions usually made the Earth flat or at best only slightly curved. By 500 B.C., however, the observational data clearly showed that a flat Earth was not a reasonable model. If the Sun and Moon are round, then the Earth must be round, too. Sailors and other travelers reported that certain bright stars appeared higher or lower in the sky as one traveled northward or southward across the Earth. This can only happen if the travels are made on a curved surface. As ships sailed out to sea it was observed that they did not disappear by growing smaller, but rather disappeared as if they were sinking into the ocean - first the keel disappears, then the lower part of the sail, then the "crow's nest" or mast tips. Again this can only happen if the ships are sailing over a curved surface.

The Greek philosopher Aristotle (ca. 384-322 B.C.) used the arguments cited above plus one more. Aristotle concluded the Earth must be spherical because of the shape of the darkened shadow of Earth that moves across the face of the Moon during lunar eclipses. By this time period it was fairly well accepted that eclipses of the Moon occurred because the Earth was blocking the Sun's light from the Moon. No one had ever reported the shadow of the Earth that falls on the Moon to be any other shape than circular. Aristotle argued that the only geometric solid that could always give a circular shadow, no matter how it was oriented in space, was a sphere.

This activity will allow experimentation with common shapes to determine if Aristotle was correct.

PROCEDURES:

1. Set up the projector and screen so that the various objects can be placed in the light beam and shadows will be cast onto the screen. (An alternative might be to take the students outside on a sunny day and let them watch the shadows of the objects on the ground or sidewalk.)

2. Place the child's block in the light beam and observe the shadows cast by it. Turn the block in as many ways as is possible to see how the shadow changes with orientation of the solid. Under a column labeled for each of the solid shapes with which you are experimenting, draw a picture for each different shadow or describe each different shadow seen as completely as possible.

3. Repeat the above step with each of the other solids and record your observations in the same manner as in Step 2.



DISCUSSION QUESTIONS:

1. Which of the geometric solids produced circles as shadows? Were these circles the only shadows produced by these solids?

2. What common characteristics do the solids have that produced circles as shadows?

3. What would you have to do with the solids that produced circles as shadows in order to always produce shadows?

4. Is the idea that the Earth is a sphere, a theory or a fact?

5. Why is knowing the shape of the Earth important?

6. How does this exercise with the shapes prove that the Earth has to be spherical?



Return to Shape of the Earth


DEVELOPED AT



Under a Grant from

THE NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
PRE-SERVICE EDUCATION PROGRAM



Written by:
Ronald A. Johnston
Assistant Professor
Department of Natural Sciences
Fayetteville State University
1200 Murchison Road
Fayetteville, NC 28301


Sponsored by:
Mathematics and Science Education Center
Fayetteville State University
1200 Murchison Road
Fayetteville, NC 28301
Leo Edwards, Jr., Director