We really enjoyed watching Kelsey Houston-Edwards’s latest PBS Infinite Series video last night:
We’ve played around with a few ideas about altering Pi a few times previously. One was with Vi Hart’s “Pi = 4” video in this project:
A second time was a super fun series of projects on 4-dimensional shapes inspired by a tweet from Patrick Honner. That complete series is here:
Today we explored the 2-dimensional idea in Kelsey Houston-Edwards’s video in 3-dimensions using 3d printing.
First, though, I asked the boys what they thought about the latest PBS Infinite series video:
Next we took a look at 6 different “spheres” in 3-dimensions which were defined using the different way of measuring distance Kelsey Houston-Edwards introduced in her video. It is really fun to hear kids talking about these shapes, and even more fun to be able to actually hold these shapes in your hand!
The last thing we did was look at the 6 spheres all together. My younger son noticed how much bigger the shapes got as you moved from the L-0.75 norm to the L-4 norm. My older son noticed that some of the shadows of the shapes looked pretty similar even though the shapes didn’t look the same at all:
This was a really fun project to prepare. It is really fun to show kids ideas from advanced math that the wouldn’t likely see in school. It is also really fun to hold these strange shapes in your hand! Lately we’ve been using the F3 program to help us make objects to print – it was a really lucky coincidence to see the new PBS Infinite Series video *after* I learned to use the new program. It took less than 5 minutes to make the .stl files for the 6 shapes 🙂