Astronomers have tried to look for evidence of curvature by studying the number of galaxies they can see in the distant universe. As they look out they expect that the number of galaxies that they can see should stay about the same as right near them, or in other words the galaxies should be evenly distributed throughout space. If the universe is positively or negatively curved, however, the evenly spread galaxies will either appear less or more dense far from the observer.
- Rulers
- Paper
- A spherical surface which can be written on and cut up such as the domed top half of a 2 liter bottle, or ideally the plastic lid which is often placed on top of frozen yogurt or slushies.
- Stretchy material in square pieces about a foot per side or a hyperbolic sheet made as described here.
- Pens which can mark on the spherical surface and material.
- Have the students make evenly spaced marks on the domed surface using the rulers and pens.
- Also, have them make evenly spaced marks on the flat paper.
- Have one student from each group hold two opposite sides of the stretchy material up and another student hold the other two sides down to form a surface which approximates a hyperbolic one. Have a third student mark evenly spaced marks over the surface of the stretched surface. If you have a hyperbolic sheet try making the marks as evenly as you can without destroying the surface.
- Now, because these are representations of 2 dimensional surfaces in 3 dimensions we need to make flat maps of the locations of these evenly distributed particles. To do this, simply leave the flat paper map flat, let the lycra material go and lie flat on the table and take scissors and cut radial slits in the plastic lid so that it too can lie flat on the table. If you have a hyperbolic sheet simply observe the sheet from above. For further discussion of mapping between dimensions see below.
- Have the students come up with a trend which describes the new location of the "evenly spread" dots. Starting from the center of each surface and moving out in rings describe the density of the dots. Students should find that the dots on the spherical surface now grow less dense as you move from the center, the dots on the plane surface remain at the same even density, and the dots on the "hyperbolic" surface grow more dense towards the edges.
- Explain to the students that Princeton Physicists have tried to examine the curvature of the universe by plotting the concentration of galaxies which are assumed to be evenly spread throughout the universe. Their results seem to be closest to the flat paper model suggesting that the density of the universe is nearly critical.
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