This Could Have Been an Email - Teaching Edition

I have two pet peeves in this world: people wasting my time and me wasting other peoples time. I recently realized that I've been wasting my students' time and my time by creating videos that could be Blackboard announcements. I've decided to stop making as many videos and focus on other ways of connecting with students.

During my online teaching professional development, I was taught to use introduction videos to help students start to form a connection with their instructor. Of course, I can't stop with just one video. I have to make a video for each week of the course. Since I'm terrible on camera, these videos take longer to make than is reasonable. Also, no one watches the videos after the second week of the semester.

To try to maintain some personal connection, I plan to record the weekly posts as an audio file and upload it next to the script. That way students can choose either option. This also covers my bases for accessibility. Because audio files are easier to edit and looking good on camera isn't an issue, the whole process goes faster.

A welcome message for Liberal Arts Mathematics. There is an audio file player above the written text.
Student view of a finished welcome message.

Also, it is possible to use the recording process to create videos as well. It works pretty well to solve a problem and scan each step in the process. I can create PowerPoints with the scans and other text and then save the whole thing as a series of images. A video editing program can assemble the images with the narration. It is possible to do this entire process in PowerPoint, but I like to edit the audio first. This post from the Audacity wiki shows exactly how I edit my audio.

Long term, I'd like to assemble all of the audio recordings into a single file for students to download. This is an idea I picked up from Michael Wesch. It may not work as well with math as it does with anthropology, but that's a problem for later.

Since my perfectionist tendencies have to be appeased somehow, I decided to build a recording area in my messy garage. With $45 worth of PVC pipe and Harbor Freight moving blankets, I managed to pull something together. There is a frame built out the PVC pipe and some fittings. The blankets are clamped to the frame. It's not professional quality, but a little effort goes a long way.

Two shelves hold some moving blankets.
I can fit myself, a microphone, and a recorder in there.

A piece of lumber holds up a PVC pipe frame. A moving blanket is clamped to the frame
Close-up of the frame and blankets.

One-Upping the Stand Up Mathematician?

In October of 2021, Matt Parker - number 3 on my list of YouTube man crushes - and Hannah Fry released a video on YouTube demonstrating how to measure the radius of the Earth using a tall building and protractor. Their attempt was moderately successful despite facing several obstacles. On a recent family vacation, I realized I had the perfect opportunity to make a more accurate measurement. Keep reading to see how our estimates compare.

Hannah and Matt

The process outlined in the video requires an observer to climb to a high point and measure the angle of declination down to the horizon. Using your elevation, the angle of declination, and some surprisingly elementary trigonometry, you can calculate the radius of the Earth. This method was devised by 10th Century mathematician al-Biruni. Using his method, al-Biruni was able to calculate the radius with surprising accuracy.

Hannah and Matt had several difficulties to overcome in their experiment. The main problem was getting their measuring equipment through building security. Additionally, Matt insisted on measuring the height of The Shard through trigonometry.

The duo's results are:

  • Height of observation deck: 263m (Actual: 244 m)
  • Angle of Declination: 1.5 degrees
  • Radius of Earth: 875 km (Actual: 6371'ish km)

Visiting the Perfect Location

Visiting the perfect location for this experiment was a lucky coincidence for me. There was a mountain with high elevation located close to the sea on our vacation itinerary: Haleakala. The lack of building security is a plus.

Haleakala Visitors Center sign. Elevation 9740ft or 2969 m.
Photo Credit: Emily Sears

Standing on the top of a volcano was the one experience I wanted out of the trip. We took a tour bus up for sunrise. The pickup time was 2:30 am, which sucked. The rest of the trip was amazing.

There was a healthy crowd at the Visitor Center. Fortunately, everyone was respectful. That is not always a guarantee, but the Aloha Sprit was with us tourists. The light of sunrise played nicely with the cloud layer below. I was able to poke around the crowd to get a few shots. The thinner air at the top made moving around more difficult. I hiked up to the higher observation area, and had to stop every few minutes to catch my breath.

Silhouettes of people watching a sunrise over Haleakala.
Silhouette of the Crowd. Photo Credit: Chris Sears

The sun rises of a cloud layer.
The view from the top. Photo Credit: Chris Sears

The clouds enhanced the natural beauty, but they worked against my secondary objective for this trip. Finding the horizon turned out to be a problem. The clouds started to break enough to see the ocean. If we had stayed for an extra half hour or so, the view of the horizon would have been clearer. With the tour bus loading, I made the best measurement I could.

A measurement of 0.95 degrees seemed good enough for me. I remembered that Hannah and Matt should have measured around 0.5 degrees from The Shard. A larger angle is expected from a higher height. I was happy with the result. My family was happy I stopped talking about math for the rest of the morning.

View of the Pacific Ocean from Haleakala. Clouds obscure the horizon.
The view of the horizon. Photo Credit: Chris Sears

A digital level reads 0.95 degrees.
0.95 degrees was the best I was going to get. Photo Credit: Connor Sears


After returning to the mainland, it was time to crunch the numbers. Here are the results:

  • Height of observation: 2960 m (Rounded to three significant digits and adjusted for standing below the Visitor Center)
  • Angle of declination: 0.95 degrees
  • Radius of Earth: 21500 km (Actual: 6371'ish km)
Well, that is disappointing. Matt and Hannah were off by 86.3% of the actual value. I was off by 238%. Looks like I'll be eating the humble pi tonight.

It is possible to work backward to find the proper angle measurement for a height of 2.96 km. I should have measured 1.75 degrees. This is one time where aiming for the clouds was the wrong thing to do.

The video below shows how I made the computations.