Dr. Sarah's Geometry of our Earth and Universe Part 2

In class on Friday, we began the geometry of the earth and universe segment. You choose a research problem and presented your intuition. We discussed the fact that now that you have seen some of the ways that mathematicians do research, you are going to do some research in mathematics the way that mathematicians do. We first think about the problems by ourselves. Then we consult books and journals, and rethink the problem using ideas from other sources to help us. Eventually we might talk to an expert in the field and see if they have ideas to help us. Recall that this process can be frustrating, but that it is the struggle that leads to deep understanding. (For example, Wiles describes doing mathematics as first entering a dark mansion and bumping into furniture. After a while he gets used to the dark and stops bumping into the furniture. Finally, after about 6 months, a light switch comes on and he sees where he has been all along.)

Dr. Sarah Models the Process for Problem 0

Problem 0 How could we tell that the earth is round instead of flat without using any technology (ie if we were ancient Greeks)?

Step 1: Dr. Sarah Initial Intuition for Problem 0

Mathematicians first think about problems by ourselves as we explore our initial intuition. While our intuition may not lead us to a "correct" solution, this process of exploration is imperative for our understanding.

Initial Intuition
Problem 0
by Dr. Sarah

Problem 0: How could we tell that the earth is round and not flat without using any technology (ie if we were ancient Greeks)?

For my problem, I am asked how we could know that the earth is round and not flat without using any technology. I will attempt to answer this question by using only my initial intuition.

As I first thought about this problem, it occurred to me that if we traveled around the earth and fell off of it while we were traveling, then we would know that the earth was not round. On the other hand, if we never fell off while traveling, then we could not tell whether the earth was round, flat or some other shape. It could still be flat but perhaps our travels had just not taken us to the edge. Historically, I think that people thought that the earth was indeed flat, and that a ship could fall off the edge. I then realized that this approach would not solve the question, because it would never allow us to determine that the earth is actually round.

I next thought about trying to find a definitive method to tell if the earth was round and not flat. If we could travel all the way around the earth, being assured that we were traveling in the same direction all the time, then this would differentiate our living on a round earth from living on a flat earth. Yet, we are not allowed to use any technology to help us, so a compass would not be allowed. Given this, I'm not sure how we could know that we were traveling in the same direction. Hence, I decided that while this was a good idea, I could not make the method work without technology.

Finally, I gave up on the idea of traveling to reach a specific destination, and started to think about the constellations. If we travel to different places on the earth, we see differences in the stars. For example, constellations look very different in the northern hemisphere than in the southern hemisphere. Also, even within the northern hemisphere, the north star is in different positions in the sky. This would not occur if the earth were flat and would indicate that the earth was round.

This concludes my initial intuition on Problem 0.

Note: You already completed step 1 in class on Thursday

Step 2: Dr. Sarah's Research for Problem 0

After developing initial intuition on a problem, we consult books and journals, and rethink the problem using ideas from other sources in order to help us.

On the web, using google.com, I searched for
+round +earth +flat
but too many pages resulted. Next I searched for
+round +earth +flat +"how can we tell"
which returned about 46 pages. After skimming through them, I decided that the following would be the most relevant .
Read these - you are responsible for the ideas in them!
Round Earth feels flat
Why are planets round?
Was Columbus the first person to say the Earth is round?
How we know the Earth is round
How Do We Know the Earth is Round?

Note: While I have modelled the research process for you, I have not created the corresponding report.