I’ve wanted to do this experiment ever since I was a sophomore in high school, and heard of how Eratosthenes was able to measure the circumference of the earth just by looking down a well in a couple of towns in Egypt 2000 years ago. A few years ago, when I was at a boarding school, I even got up on stage and challenged the students to come with me to measure the earth with a stick, but somehow, I never followed through.

This year, I had the equinox marked on my calendar, and contacted my reliable, physics partner in crime, Frank Noschese, who I had just spoken to for the first time on Wednesday, learning his name is pronounced No-skay-se, and not Nose-chese).

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Anyway, we thought it would be great to give skype a shot, and try reproduce the Eratosthenes measurement between our two classrooms. Our initial thought was to do this in a total open-ended manner. Here’s a stick, and I think you can measure the earth with it. Go to it. This was over-estimating our kids ability to work this out. Some silly errors that came up:

• My kids didn’t use a level to make sure that their meter sticks were perpendicular to the ground, and consequently, our measurement was too long, which led to Frank calculating a ridiculously small radius of the earth.
• As a result we decided to fix this by having students go out and re-take the measurements using a level while the class waited. This produced to measurements that were much better.

It didn’t take too much for our kids to come up with the following drawing:

Here, students got a bit stuck, but they got unstuck when we asked them to find the angle the sunlight made with the meter stick. Trig functions started to fly, and pretty soon, the kids figured out that the angles were 33° and 42°. Here, rather than try to get the kids to make the geometric argument that they’d just measured the latitude, I tried to get them to think what would happen to the stick at other places, using the following conversation

me: what do you think the angle between the sun ray and the the meter stick would be if you were at the equator on the equinox?
s: the angle would be 0° because there wouldn’t be a shadow.
me: what if it were at the north pole?
s: it would be 90°, because the shadow would go on forever.
me: so what happens to the angle as you go up in latitude?
s: it gets bigger, so when the angle increased from 33° to 42°, it increased by 9°, which is about 1/10 of 1/4 of the way around the globe.
me: so if I tell you the longitudinal distance between ATL and NYC is 500 miles, what can you do with this?
s: Oh, I’ll just multiply that by $10\cdot 4=40$, and come away with 20,000 miles.

And just then, Frank’s class arrived at the very same thing.

Here are some observations about the whole skype thing

• Students LOVE connecting with other kids. My kids had so many questions—do they watch Glee? Do they know my friend in NYC? What is their school like?
• Students have lots of stereotypes at play, even though my and Frank’s kids are pretty much identical. North vs south, private vs public, etc. I hope talking to kids who are from a different part of the world helps our kids dispel these stereotypes, but they can also manifest themselves as the occasional rude comment or two.
• I should have spoken to  a language teacher about how to better moderate a skype discussion. A 30 on 15 discussion tends to chaos. If we do this again, I think Frank and I want to have small groups of kids making presentations to the other class.

But overall, I think the experiment was a success, and I’ll let my kids reactions speak for themselves:

• Talking to kids from New York was pretty amazing. I never thought that our science class would reach out past the <school> boundaries. Working with kids in New York over the internet was not only cool, but it allowed us to access data we couldn’t have taken. Together, both of our classes discovered the answer to a difficult question. Who would have thought we could measure the circumference of the earth with a stick?
• I learned that science is definitely not confined to our classroom. It can reach world wide, and with some simple calculations anyone can measure almost anything.
• It was amazing to measure something as great as the circumference of the earth using just a yard stick….. It was just a really cool knowing that you can get knowledge such as that by finding out yourself.
• Skyping with the class from New York was AWESOME!!!! It was so cool because even though we dont know them, we were really interacting with people all the way from New York and working together to find out information.
• I learned a ton! I learned all about the tilt of the earth and shadows and how on that particular day in the year, you can measure the circumference of the earth because it is the first day of fall which is in the middle of all of the other seasons. The earth is tilted just right to do the experiment.
• It was awesome to Skype with another physics class because we could see how similar to us kids from another part of the country are. And we got to do some physics…
• Measuring the circumference of the earth was so much fun and interesting!
• It was really interesting and unique to measure the circumfrence of the earth with a stick. I never thought that it was possible, but it was! At noon, on the first day of fall, our class went outside and measured the shadow a meter stick made on the pavement. We had to choose a flat surface and once we had collected our data, we averaged the groups measurments to come to a conclusion that the shadow was around 80cm.
• It was really fun to skype with the physcis class in New York. Knowing that they were conducting the same experiment at the same time we were was really cool, and then to be able to discuss it with them live was awesome.
1. September 26, 2010 11:24 am

And you don’t really need to do this measurement on the equinox (this just makes it really easy for kids to see that the shadow at the equator would be 0°). In many ways, you might dispel more misconceptions by doing at some other day and time when the sun isn’t directly overhead the equator.

2. September 26, 2010 6:16 pm

You guys are awesome. This takes a traditional dry lecture and gives the students a chance to take data and reach conclusions of their own. I am totally stealing this for my astronomy class. Have you shown this to your history teachers? I think it would be a great interdisciplinary exercise.

3. September 26, 2010 9:07 pm

Not that is a cool use of skype. I may have to do this with my kids when I do astronomy next semester.

4. September 30, 2010 11:49 pm

Neat use of technology. Back when I helped teach Field Geology we did the Eratosthanes thing but were limited by the fact that our measurements couldn’t be taken simultaneously. We’d take a measurement in Yellowstone and then another two weeks later in Moab. The sun’s position in the summer sky was different enough in that two week interval to introduce a sizable margin of error. But using Skype to involve students in two locations at the same time . . . that’s very cool.

Maybe if I had been in a physics classroom like yours in high school I wouldn’t have ended up as an English teacher.

• September 30, 2010 11:56 pm

Thanks Clark. Yes, I used to always feel I had to wait until the equinox to do this, but you’re right, Skype makes all this unnecessary. Now we should do some parallax to figure out the distance to the moon or something like that.

5. October 21, 2012 1:30 pm

I love this one, and want to share it in a session. The drawing in the middle of the post seems to be a broken link right now, though.