As the Egyptians did not
draw three-dimensional shapes, it is likely they derived the solution through
similar triangles.
Lastly, we discovered a generalization
to the equation to extend our problem to frustums of n-sided regular polygon
bases:
I really enjoyed this project
as it was an interesting look at how ancient Egyptians likely solved
mathematical problems. It demonstrates that there are different methods to
solve a single problem, and limited by techniques developed at the time, we can
see that it is still possible to solve this problem using the same method they
solved in the past. I can see this activity be incorporated in a classroom
learning about surface area and volume, which can teach students to think
creatively “outside the box” when determining frustum volumes by separating the
frustum into different three-dimensional shapes.
https://docs.google.com/presentation/d/19k7213cygiKP1h1O11EwXUJ8k5JpRw3ubVyEAjUGMWg/edit?usp=sharing
Hi Matt,
ReplyDeleteGreat presentation! It's very interesting to see how complex of a problem calculating the volume of a pyramid is especially since it seems like such a basic mathematic concept in today's schools. its amazing to me how they used similar triangles which seems like a more complex solution but since they had never seen pyramids drawn as we do in modern mathematics it likely seemed like an elegant solution to them. I find it interesting what people will say about our mathematics in a few thousand years!
Winston, thanks for your very thoughtful comments and appreciation of this interesting project!
ReplyDeleteMatt and group, well done -- and I appreciate your thoughtful reflections on the project too.