This year, my school is doing a Bring-Your-Own-Device initiative. I’m super excited because it means that I can use GeoGebra and Desmos in class!

One of my favorite things to do in Physics is to discuss Eratosthenes’ estimate of Earth’s Circumference. It’s a good early activity to check how much they remember from Geometry, and show them an example of how math knowledge can be applied to solve real world problems. I think this year, it will serve as my intro to GeoGebra too!

**Problem: **

Eratosthenes calculated the circumference of the Earth from his home in Alexandria. In the city of Syene to the south, there was a deep well that served as a landmark. Eratosthenes knew that on one day each year, at noon, the sun would be directly overhead, and the water below could be seen. (This day was the longest day of the year, the summer solstice.) On this day, in Alexandria, Eratosthenes went out at noon, and observed the shadow of a vertical landmark. The angle between the base of the landmark and the end of its shadow was measured at 7.2 degrees. Eratosthenes estimated the distance between Alexandria to Syene, and used these values to make his calculation.

- We will estimate the distance from Syene to Alexandria as 800 km.
- We will assume the Earth is a perfect sphere.
- We are going to ‘guess’ the radius and circumference of the Earth, and use Geogebra to match our situation to Eratosthenes’

**Click the picture to go to my Geogebra file**

**Extension: The sun’s rays can be adjusted to show how to solve this problem with shadows in both cities.**