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course Phy 231
PHeT estimationI spent a few minutes on the
Not surprisingly, I did quite well on linear estimations, adequately on 2-dimensional estimations, and pretty poorly on 3-dimensional estimations.
On every single 3-D object, I drastically underestimated how many of the smaller object would fit into the larger object-- even after I caught on and tried to override my instinctive guesses and start inflating them by 50% or so.
In fact, on one of the cubes, I was off by so much, I was sure there was a flaw in the program. I estimated that each surface of the larger cube would fit a 15 by 15 grid of the surface of the smaller cube. Based on that estimation, I mentally calculated 15*15*15, for a guess of just over 3000. When the answer came back as well over 9000, I got out my ruler and quickly measured, and realized it was actually more like a 20*20*20 cube. Still, that only got me 8000. I measured again, and realized, OK, maybe it's somewhere between 20 and 21. Sure enough, that got me in the ballpark. It's astonishing to realize that a .5 unit or so difference in one linear edge of a cube can change the volume by over 1000 units.
It's been a long time since I memorized the formulas for calculating volume of various geometric shapes. But I suspect that even if I knew them all by heart, my eyes and my best efforts would still betray me on quick estimations. Volume increases by much larger magnitudes than it seems it ought to if I'm just trusting an ""eyeball it"" method. "
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Very good.
I'm good as estimation, but I still have to cheat with calculational methods to estimate ratios for 3-d objects.
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