Another Exciting Math Lesson outside

I came across a fantastic BBC documentary for social studies called “What the Greeks Did for Us” which showed the innovations of Archimedes, Pythagoras, and other ancient Greeks. Something that caught my eye was around the 15:00 minute mark of the documentary- a piece on how the Greeks used geometry to drill through a mountain from either side and met perfectly in the middle.

Deciding to put it to the test for ourselves (go cross curricular connections!), I borrowed some clay from the art teacher, dowels, string and straws from the science lab and headed outside with the students.

First I explained the situation: a village of ancient Greeks is worried that they will be cut off from their fresh water supply on the North side of a mountain, if there is an attack from an enemy. They have an idea- drill through the mountain to create a tunnel. This wasn’t a totally crazy idea for the time as many aqueducts and incredibly elaborate irrigation systems had been developed. So off they set with picks and chisels. Soon, as you can imagine, they felt daunted by the task. They decided to send a team to the opposite side of the mountain so that they could double their efforts and complete the task more quickly. But how could they be sure that they would meet in the middle?

I asked the students to stick a dowel through the mountain from both the north and south and try to meet in the middle. Try as we might, no luck.

They played around with the string and dowels for about 5 minutes before I prompted them by sticking 4 of them in the ground at each quadrant around the mountain. This prompted some of them to use the knowledge of angles and degrees. They were on the right track by still needed prompting. I asked them to consider what we had learned previously about bisecting angles.

Finally, they had a square (ABCD) set up around the mountain (with string) and used point A and C as starting points for drilling. They used a square set to enter the dowel into the mountain (45 degree angle from corner post) and VOILA! they met in the middle! We “drilled”  a hole through the mountain, stuck in the straws and poured water through the straws. Much to our astonishment, water came all the way through!

All in all, this was a complete success and an incredible way to show the importance of circumference, perimeter, angles and bisecting angle. Not to mention a great activity for outdoors!