We had another science class. We reviewed Thales (first scientific explanations, amber can attract all kinds of stuff, magnets can only attract iron). We reviewed our shapes (spheres, hemispheres, cylinders, cubes). We talked about circles changing to ellipses to the observer as the angle of the paper is changed. I showed that the shape of a sphere when it has been cut is a circle. (These are great for the talks about shapes.) We talked about how the face of a cube is a square. The kid who's advanced in math knew that the difference between a cube and a square was that the cube was 3-dimensional. For the other kids I tried to emphasize that area is flat (um, yeah, we'll get to the other stuff later) and that cubes take up space and have volume. Those are the next two concepts I need them to understand: area and volume. After all, density it coming up.
We also talked about 45 degree right triangles again. We talked about how it is half of a square, on the diagonal, and we know that both of the legs of the triangle are the same length. I then used three different sized triangles and pointed out that no matter how big or small the triangle gets, as long as it has the same shape, we know the two legs of the triangle will be the same length. I mentioned that this may have been how Thales could have measured the heights of tall buildings. He could have waited until the shadow of a smaller object was the same as its height and then measured the shadow of the larger object to find its height.
This talk was a summation of the evidence that the Earth is a sphere. The kids seemed rather shocked that people 2400 years ago would have known (without spaceships, satellites, and round-the-world cruises) that the Earth was a sphere. I got most of my information from the first few pages of How Did We Find Out the Earth is Round by Isaac Asimov.
We started by talking about some of the ancient ideas about how the sun rose and moved across the sky every day. Some people believed it was carried by a chariot, that it would set into the ocean and be sailed back to the east to begin its trek again, or that it would die every night to be reborn in the east. They liked that one--they spent the next few minutes performing their miniature Oscar-winning dying scenes.
We talked about how Anaximander thought the heavens had to be a sphere because they move from east to west, but there was one point (the North Star) that did not ever set. Then we talked about the number of different ideas that people had for the disk of the earth; that it was smaller than the sphere (but noone seemed to fall off the edge and why didn't the oceans drain?), or that it extended to the celestial sphere (and people could go and visit the actual place where the stars and sun met the disk of the Earth and lift up the starry curtain--more antics about the possible death that would ensue). Neither of those ideas were satisfying to the Greeks. [I used a large, decorated, clear glass serving bowl to show the sky and the north star was the center of the bottom. I used a circle cut out of paper to represent the 'flat Earth.' I rotated the upside-down-bowl to show the stars (the decorations) turning from east to west and how the north star (the center of the bottom of the bowl--I should have taped a star to it) didn't move. Most of these kids were in the astronomy class last year so they had the experience of seeing the constellations being in about the same place night after night, but also how the constellations would move across the sky as the night wore on.]
The Ancient Greeks were also discovering that the moon looked different depending on where it was in relation to the sun. If it was on the same side of the sky as the sun, then it was dark to us. If it was on the opposite side than the sun, it was fully bright, with all of the variations as it moved between. They figured that if the moon changed shape with part of it dark and some light, that it must not give off its own light and was lit up by light reflected from the sun. The changes of the shape of the moon and how the curve was always circular showed that it was a sphere. [I used a flashlight and a small ball to give them the idea, not dark enough for a real demonstration, of how the different phases looked. Since most of the kids had taken astronomy, this was old hat to them and only a reminder.]
The sun never changed and was always light so it must have light of its own. They could also tell that the sun could shine on the Earth just as well from every location. The sun also shined on the moon from every location. The sun also had to be a sphere in order to shine equally from all different directions. [This time I took the flashlight and moved it around the 'Earth' (a different ball) with the moon laying next to it, and they could see how the flat circle of the flashlight did not illuminate the spheres the way the sun does.]
So the stars were on a celestial sphere, the moon was accepted as a sphere with the evidence of their observations, and the sun was accepted as a sphere based on their observations, then what about the Earth? Did that mean the Earth was a sphere? The Greeks knew that the Earth wasn't like the stars--we don't have stars under our feet (more antics of burning yourself by picking up starstuff under your feet). The Earth isn't like the moon, it's not white all around us. And the Earth is definitely not like the sun since it's not glowing (and we had the death throes again). So what evidence could show us if the Earth was flat or not?
If the Earth was flat, the stars would never seem to change location (apart from rising and setting). That was not the case though. As a person traveled north, stars they used to be able to see at the southern horizon had disappeared below the horizon. If they traveled south, they realized that stars at the northern horizon moved so they couldn't be seen. (From east to west, of course, the stars did not have a fixed position, so there was no easy landmark to notice if they changed based on location.) The only way that could be explained was if the Earth curved as you moved from north to south. [Either the kids were very quiet, or this really didn't hit home. I tried using my flat circle as the circular Earth to show that walking toward the 'north' wouldn't change the perspective of the stars but that curving the circle (I actually did bend it) would make a person look at a different area of the sky. What I should have done was to draw examples of the same star patterns from different lattitudes and show how they're closer to the horizon and also drew two circles on the blackboard--one for the celestial sphere and another for the Earth--with a little stick figure looking along the tangent line to the edge of the circle at that location to represent his line of sight and how it would hit different places of the celestial sphere.]
So the Earth, Anaximander thought, was a cylinder. Now that seemed to have its own difficulties. Why didn't it look curved? Why didn't you slip as you moved toward the curved section? Why didn't the water fall off? There seemed to be almost as many questions. [I used a formula can as my Earth now.]
As for why it didn't look curved, just think about how a large ball would look to an ant. From the ant's perspective, it would look pretty flat. The Earth is very large and we are small in comparison. In our view, it could look flat. [I didn't, but it could help to have a beach ball to illustrate this point.]
The cylinder theory was tested at sea. If the Earth was flat, then things that move away from you would get gradually smaller and smaller and then no longer be visible. So when observing ships leaving and then moving toward the horizon they watched carefully to see what happened. Every ship seemed to go deeper and deeper until they couldn't see the ship itself, just the sail and then that too sank. The ships weren't flooded, for most do return. And oddly, they didn't just sink when moving to the north and south, but when heading east and west too. So the curvature wasn't just in one direction, it was in all directions. The only shaped that curves equally everywhere is a sphere. [I used paper circle and a picture of a ship that I cut out before class. I moved the ship from the center of the circle and showed that it would just get further away. I then used the formula can and took my model ship over the north and south direction of the cylinder and showed how the ship dropped out of sight. Then I took it east to west and showed that it couldn't drop out of sight on the cylinder and we then switched to the ball again and we could see how it dropped out of sight in every direction.]
That wasn't even all. There was still another bit of evidence to clinch the deal. The final evidence relies again on the sun and moon. We talked about the sun and moon going around the Earth and that the moon could be on the opposite side of the Earth than the sun. When the Earth gets in the way, that's when there is an eclipse. Eclipses can happen in different areas of the sky. In every single case, the shadow of the Earth has a circular edge. If the Earth was a flat circle, the shadow cast would have to look elliptical when the angle between the three objects changed. Only one shape has a shadow that always looks like a circle from any angle--a sphere. Philolaus was convinced and gathered up all of the evidence and pronounced for the first time that the Earth was a sphere. (Note: Aristotle ~350 BC came up with the idea that because the Earth is a sphere, everything must be attracted to its center and people stopped wondering wny the water didn't run off.) [I taped a smaller circle to the blackboard (the moon) and used another circle (the Earth) to make a circular shadow on the 'moon' with a flashlight. Then I changed the angle of the flashlight and the 'Earth' and the shadow on the moon was obviously elliptical. I then used a ball to shine a shadow on the 'moon' and I changed the angle with the flashlight and rotated the ball and the shadow was always a circle.]
On the blackboard:
Anaximander ~560 BC
Heavens were a sphere
Earth is a cylinder because stars changed location as you moved North and South
Philolaus (fil-oh-lay-us) ~450 BC
Earth is a sphere
Activity: There were no lab activities that really lent themselves to the subject matter. I found a book called Science Crafts for Kids that had some good ideas and a few great ideas. I had been preparing for one of the crafts and saved an oatmeal container and a few formula containers (cardboard sides required). Cut out three arches around the sides so that there is a lot of light and some large openings to get your hand through (there should be three approximately inch-wide legs holding up the top). Paint and decorate the container (we didn't have time to do that). Loosely lay clear cellophane over the top and then push it down slightly in the middle. Wrap a rubber band around the top of the container to secure the cellophane. The pour water into the cellophane and place an object underneath to see the magnification. It's not much (about 2X). The kids ooh-ed and aw-ed for about four seconds before realizing it didn't really change much. Here's another type. One thing I mentioned the parents can try is changing the depth of the water in the top and then seeing if that affects the magnification. I didn't do it myself, so I don't know.
The kids were a bit rowdy because I had been letting them get a little crazy in the last couple of classes, but this time it was actually distracting and we ran out of time for our activity.