Let no one ignorant of geometry enter -- Plato's Academy
The first thing that I found interesting was when the teacher presented the various figures and how they were interpreted differently. Kind of knowing where the teacher was going, I thought about the different ways they could be interpreted, and I found that each of the teachers presented seemed to be echoes of my thoughts. However, one thing that was very interesting was that one teacher noted that some of the other teachers didn't revise their picture whenever the picture was turned upside down or differently or whatever. And one teacher made the comment that he didn't draw the picture or the figure because it was the same figure only it had been turned, which is reminiscent of typical geometric transformations – specifically a rotation or a flip.
I also found it interesting how they made the comparison between trying to use English language to transmit what is presented in a precise geometric figure – again, as they always say a picture is worth a thousand words.
I also love the fact that one team was using a clock to determine the position of those figures. What they were actually doing was using a coordinate system that identifies location of certain things in a two-dimensional space.
I also enjoyed the folding exercises as a paper, because I'm a big origami guy. I found one question quite ponder some. When the teacher asks why does folding generate perpendiculars, midpoints, altitudes, and perpendicular bisector;I found it to be a profound thought which I kind of came to the idea that a flat piece of paper is a two-dimensional plane correct, Cartesian coordinate system, X-Y systems, all those types of things ;but however, it has the added benefit of being able to transform into a 3D dimension which allows us to make these determinations. And it all is an indication of some sort of measurement. I like to quote that one person says is that those geometric definitions quote “follow the fold.” I also enjoyed the abstract conversations about the infinitesimally small aspects of a point definition that has no depth or width -- including analogous discussion of planes. Those were always wonderful discussions that I had with students when I was teaching geometry.
