This chapter is about twelve million times more interesting than the last one. At least, I find it infinitely more appealing. There's something so elegant about those bisections and inscriptions. It makes complete sense, both visually and logically.
I was at first unable to grasp why you can't trisect an angle, but now I think it makes sense. u It's interesting that the pictures for angle bisection (how to form a triangle, pentagon, etc.) all have 3 circles in them. You think of Bisection as being the division into 2 equal parts of a whole, which it is, but geometrically it seems a third circle is necessary h } $ ( - . = E ` a e g k # J ! ' ^ @ ! 2 3 ; < C U V l m x y f g 8 9 ! ! ! !
Inecessary as a kind of reflector for the symmetry.
Some of the numerical relationships between the geometrical figures here aren't immediately obvious. I would never have instinctively believed the cube and the octohedron to be explosions or implosions--the wrong words, but you all know what I mean--of one another, but it's quite logical, and very nifty. about those bisections, , and divisionsIt makes you feel there must be other transitions, perhaps interdimensional ones, which would make just as much sense if we could only observe them from the correct (impossible) perspective. duals--
I still don't like simplexes. They just are not as satisfying, visually or otherwise, as the other figures. Maybe I'll learn to be more tolerant someday.
------------------------Anya
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