Category: Assignment Instructions (Page 2 of 5)

Comment due Sunday, April 14

After last Friday’s magnitude 4.8 earthquake centered in New Jersey, I became curious about how linear algebra is applied in earthquake science. Most of what I found online was not quite relevant for us: the algebra often referred to is not linear (for example, when using triangulation to locate an earthquake’s epicenter, a system of quadratic equations is used… even ChatGPT got confused about this when I asked it for help).

However, I did find one topic that appears to use linear algebra: Geiger’s method for locating the hypocenter of an earthquake. We commonly refer to the epicenter of an earthquake as its location, but the epicenter is a point on the surface of the earth; an earthquake actually originates at some depth below the epicenter at its hypocenter. So, while the epicenter requires only two spacial coordinates, the hypocenter requires three spacial coordinates.

I am not an expert, but I have found a few resources that should help us understand Geiger’s method for locating the hypocenter of an earthquake:

• This assignment from an earth sciences class at the Saint Louis University Earthquake Center (this looks like a draft, watch out for typos!),
• This article (if you have seen partial derivatives in your differential equations or Calculus II class, this might make more sense to you),
• This article (the section on Geiger’s method looks similar to the section on Geiger’s method in the previous article).

For this assignment, you do not have to read any of these resources thoroughly (unless you want to). Read just the section on Geiger’s method in one of these resources (or another one if you find one) and try to understand:

1. what the variables represent,
2. where the equations in the linear system and/or matrices come from,
3. what the solutions of the linear system and/or matrix equations represent,
4. the steps in the procedure (this is an iterative method, which means it’s probably applied more than once).

By the way, some of these resources mention finding the “least squares solution” of a matrix equation; you can read more about that procedure here.

Don’t worry about understanding everything completely or getting everything right. Comment on this post with your ideas about items 1-4 above. If you’re not confident about one or more of them, no problem, you can just say so. Read your classmates’ comments and comment if you agree or disagree with any of their ideas. This should be a conversation among you and your classmates to try to understand this application of linear algebra, even if that understanding is just at a surface level at first.

Comment due April 7

You may have heard that we will have a solar eclipse in the afternoon on Monday, April 8. Solar eclipses don’t happen all that often, so this is pretty special. While New York City is outside the path of totality (where the moon will totally block the sun), we still can expect the moon to cover about 90% of the sun.

It is very important never to look at the sun during a solar eclipse… doing so can severely damage your eyesight!

In anticipation of the solar eclipse, you’ll complete a short activity to help you understand the geometry of solar eclipses.

Watch the short animation above and the two short videos linked here. Then on your own piece of paper, set up and complete the three tables in the Modeling an eclipse section here. You’ll need:

• 1 sheet of 8.5 x 11 graph paper
• 2 disks approximately the size of a quarter, one to represent the Sun and one to represent the Moon at perigee
• One disk approximately the size of a nickel, to represent the Moon at apogee
• Pencil
• Ruler

After you have completed the activity, record your results in a comment below (state at which points (si, mj) where a total or partial solar eclipse occurs). Then include answers to reflection questions like:

1. Have you ever completed an activity to understand solar eclipses before? Did this activity help you understand why we sometimes have solar eclipses and sometimes don’t?
2. Are you familiar with the difference between solar eclipses and lunar eclipses?
3. Do you plan to try to see the eclipse on April 8? Do you have a plan to protect your eyes?
4. Do you have any funny or interesting stories about seeing an eclipse?
5. Can you imagine what it would be like for a person living in an ancient civilization to experience a solar eclipse? How do you think they would have felt?