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"One of the bad things about pictures is that they are almost always overspecific. One cannot make a picture of "an arbitrary triangle": as soon as one has made
by daralthus 11y ago
"One of the bad things about pictures is that they are almost always overspecific. One cannot make a picture of "an arbitrary triangle": as soon as one has made it, it has either an obtuse angle or not, whereas for "the arbitrary triangle" the property of having an obtuse angle is explicitly undefined."
Still one can make a picture of all the arbitrary triangles at the same time and in an interactive visualization explore them to get the complex behaviour and constrains the notion "arbitrary triangle" actually represent.
For a good example have a look at:
http://worrydream.com/LadderOfAbstraction/ http://worrydream.com/LadderOfAbstraction/
- Someone 11y agoBut how do you know that, while playing with such an interactive visualization, you looked at all possible cases? Also, let's say a theorem says two lines are parallel, two distances are equal, or three lines intersect in a single point, how are you going to judge that that's the case from such a display, even for one particular choice of points?