This is great. More stream of consciousness while Guy solves math problems please.
I thought it was interesting that it was easier for me to picture the proper shapes than it was for you (I had no trouble getting the lines of my pyramid to join together, and I could easily imagine where the line for the altitude of the tetrahedron went), but you thought of the relations between line segment lengths and came up with the formulas for them much more quickly than I would have.
One thing I want to clarify though, when you said you were imagining the pyramid and dotted line, and then your mental imagine didn’t match that correctly—were you first successfully imagining the pyramid and dotted line, and then trying to also have a mental image, or when you said you were imagining did you just mean that you were starting to form the mental image? And if the former, what did this imagining consist of, other than just awareness of the abstract idea that an altitude should go from a face to its opposing point?
This is great. More stream of consciousness while Guy solves math problems please.
I thought it was interesting that it was easier for me to picture the proper shapes than it was for you (I had no trouble getting the lines of my pyramid to join together, and I could easily imagine where the line for the altitude of the tetrahedron went), but you thought of the relations between line segment lengths and came up with the formulas for them much more quickly than I would have.
One thing I want to clarify though, when you said you were imagining the pyramid and dotted line, and then your mental imagine didn’t match that correctly—were you first successfully imagining the pyramid and dotted line, and then trying to also have a mental image, or when you said you were imagining did you just mean that you were starting to form the mental image? And if the former, what did this imagining consist of, other than just awareness of the abstract idea that an altitude should go from a face to its opposing point?