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If you draw a "dotted line" from "A to C", it becomes blatantly obvious that the backside must be curved or warped in some degree (where the "dotted line" repre
by dragontamer 5y ago
If you draw a "dotted line" from "A to C", it becomes blatantly obvious that the backside must be curved or warped in some degree (where the "dotted line" represents the bottom base). Assuming that the front-faces are flat, the triangle on the top of the figure is too warped to match the readily assumed triangular base.
In fact, my brain is bouncing between many different interpretations of the base when I saw this figure (first one is a quadrilateral base, as discussed in the blogpost) I don't consider myself to be that good with geometry, but I did play with CAD for a bit back in college, which probably built my instincts up. I imagine that machinists and mechanical engineers would instinctively see the "impossibility" of flat-faces and a 3-sided bottom base.
Us computer engineers really won't work with real-world geometry enough to really get the instincts that those mechanical engineers get though. That's fine. They can taunt us with their superior geometry skills while I'll taunt them with my superior C++ skills!
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I did require the additional guidelines to see the problem. But an additional set of guidelines (ex: dotted-triangle base of ABC) would really make it more obvious.
- red_trumpet 5y agoIf the top triangle is not parallel to the base (which you picture by your method), then the two triangles don't match, even in a real picture.
- dragontamer 5y agoThe "impossible" part is trying to imagine a "flat" ADFC face. There is no such "ADFC" face that can result in a triangle in the shape of DEF. ------- To imagine what "ADFC" could possibly look like, I suggest trying to visualize the ABC-base at first, and then trying to imagine different "ADFC" faces to match the ABC-triangle with the DEF-triangles. The only way you can get this shape to look like this, is if ADFC is bent or twisted somehow. No "straight/flat" ADFC could possibly connect the bottom with the top.