We had a 2 hour school delay due to snow this morning – perfect time to . . . .
My goal for this week with the boys is to work thorough Patrick Honner’s Pi day exercise in 4 dimensions. I already did the 3d version with my older son:
Patrick Honner’s Pi Day Exercise
and worked through the 4d version on my own last Monday:
Patrick Honner’s Pi Day Exercise in 4d
The path to getting the boys to understand the 4d project goes something like this:
(1) The 4d versions of volume and surface area for a sphere involve 
(2) We have to understand some of the simple 4d shapes – I’m looking at the 6 4d platonic solids. Our Zometool set helps us understand those shapes.
By luck, we’ve already done a project on the one Platonic solid that exists in 4d that doesn’t exist in 3d:
Using Matt Parker’s Platonic Solid Video with Kids
(3) Finally, we have to come to understand the “volume” and “surface area” formulas in 4 dimensions. That is the part that I worked through last Monday after finding this awesome website:
Today’s project was mainly about point (2) above.
We started by looking at the 5-cell:
The the 8-cell, or Hypercube:
And finally the 16-cell which is a little more difficult to build and visualize. Luckily we found this helpful website:
The 16-Cell and some relatives
It was nice to have the surprise snow day today to play with these shapes!
Mike's Math Page 